Let ${\mathfrak{M}}$ be a nonstandard model of Peano Arithmetic with domain M and let ${n \in M}$ be nonstandard. We study the symmetric and alternating groups S n and A n of permutations of the set ${\{0,1,\ldots,n-1\}}$ internal to ${\mathfrak{M}}$ , and classify all their normal subgroups, identifying many externally defined such normal subgroups in the process. We provide evidence that A n and S n are not split extensions by these normal subgroups, by showing that any such complement if (...) it exists, cannot be a limit of definable sets. We conclude by identifying an ${\mathbb{R}}$ -valued metric on ${\tilde{S}_n = S_n /B_S}$ and ${\tilde{A}_n = A_n /B_A}$ (where B S , B A are the maximal normal subgroups of S n and A n identified earlier) making these groups into topological groups, and by showing that if ${\mathfrak{M}}$ is ${\mathfrak\aleph_1}$ -saturated then ${\tilde{S}_n}$ and ${\tilde{A}_n}$ are complete with respect to this metric. (shrink)

As teams become increasingly common for organizations to accomplish key objectives, improving team performance is a critical challenge for both practitioners and researchers. As researchers have converged on the notion that team performance is strongly influenced by subgroups, scholars have begun to explore how perception of subgroups influence team performance. Thus, in this study, we examined how perceived subgroups influenced the team transactive memory system (TMS), and hence team performance. We also proposed the moderating role of guanxi perception on the (...) relationship between perceived subgroups and TMS. Utilizing two-wave multi-source data from 87 working teams in a Chinese central government-owned corporation, and based on multiple (moderator) hierarchical regression analyses, our results demonstrated that perceived subgroups were a negative predictor of TMS and team performance and TMS mediated the negative relationship between perceived subgroups and team performance. That is, perceived subgroups inhibited team performance by blocking the development of a robust TMS. In addition, guanxi perception acted as a positive moderator, mitigating the negative relationship between perceived subgroups and TMS. Furthermore, the moderated mediation analysis of the integrative model revealed that the indirect effect of perceived subgroups on team performance via TMS was contingent on guanxi perception. Overall, our findings identified the pivotal role of perceived subgroups, TMS, and guanxi perception in working teams in the Chinese context. (shrink)

We study the infinitely definable subgroups of the additive group in a separably closed field of finite positive imperfection degree. We give some constructions of families of such subgroups which confirm the diversity and the richness of this class of groups. We show in particular that there exists a locally modular minimal subgroup such that the division ring of its quasi-endomorphisms is not a fraction field of the ring of its definable endomorphisms, and that in contrast there exist 20 (...) pairwise orthogonal locally modular minimal subgroups whose induced structure is exactly that of an-vector space. We also show that there exist infinitely many pairwise orthogonal subgroups of infinite U-rank. Furthermore, these constructions are carried out in the additive group considered as a module over its ring of definable endomorphisms. (shrink)

We investigate the relationship between subgroup splits, subjectively perceived subgroups, and team identification and emotional exhaustion. Based on the job demands-resources model and on self-categorization theory, we propose that faultline strength and perceived subgroups negatively affect emotional exhaustion, mediated by team identification. We further propose that subgroup identification moderates the mediation such that subgroup identification compensates low levels of team identification. We tested our hypotheses with a two-wave questionnaire study in a sample of 105 participants from 48 (...) teams from various contexts. We found an effect of perceived subgroups on emotional exhaustion mediated by team identification, but no direct or indirect effect of faultline strength on emotional exhaustion. We also could not find that subgroup identification moderates the effect of team identification on emotional exhaustion. We discuss the need for further research on the link of subgroup splits in work teams and the rise of psychological health issues and derive that measures to prevent burnout should primarily focus on avoiding or reducing subgroup perception whereas affecting the actual demographic composition of work team should be of lower priority. (shrink)

We show that type-definable subgroups of measure algebras are definable.

Given a class${\cal C}$of subgroups of a topological groupG, we say that a subgroup$H \in {\cal C}$is auniversal${\cal C}$subgroupofGif every subgroup$K \in {\cal C}$is a continuous homomorphic preimage ofH. Such subgroups may be regarded as complete members of${\cal C}$with respect to a natural preorder on the set of subgroups ofG. We show that for any locally compact Polish groupG, the countable powerGωhas a universalKσsubgroup and a universal compactly generated subgroup. We prove a weaker version of this in (...) the nonlocally compact case and provide an example showing that this result cannot readily be improved. Additionally, we show that many standard Banach spaces have universalKσand compactly generated subgroups. As an aside, we explore the relationship between the classes ofKσand compactly generated subgroups and give conditions under which the two coincide. (shrink)

We define the notion of generic for an arbitrary subgroup H of a stable group, and show that H has a definable hull with the same generic properties. We then apply this to the theory of stable fields.

In this paper we deal with the model theory of differentially closed fields of characteristic zero with finitely many commuting derivations. First we observe that the only known lower bound for the Lascar rank of types in differentially closed fields, announced in a paper of McGrail, is false. This gives us a new class of regular types which are orthogonal to fields. Then we classify the subgroups of the additive group of Lascar rank omega with differential-type 1 which are nonorthogonal (...) to fields. The last parts consist of an analaysis of the quotients of the heat variety. We show that the generic type of such a quotient is locally modular. Finally, we answer a question of Phylliss Cassidy about the existence of certain Jordan-Holder type series in the negative. (shrink)

Let ℳ be a countable, recursively saturated model of Peano Arithmetic, and let Aut be its automorphism group considered as a topological group with the pointwise stabilizers of finite sets being the basic open subgroups. Kaye proved that the closed normal subgroups are precisely the obvious ones, namely the stabilizers of invariant cuts. A proof of Kaye's theorem is given here which, although based on his proof, is different enough to yield consequences not obtainable from Kaye's proof.

It is proved that any countable index, universally measurable subgroup of a Polish group is open. By consequence, any universally measurable homomorphism from a Polish group into the infinite symmetric group S ∞ is continuous. It is also shown that a universally measurable homomorphism from a Polish group into a second countable, locally compact group is necessarily continuous.

The Cherlin–Zil'ber Conjecture states that all simple groups of finite Morley rank are algebraic. We prove that any minimal counterexample to this conjecture has a unique conjugacy class of Carter subgroups, which are analogous to Cartan subgroups in algebraic groups.

As information flows at ever-increasing speeds across technological innovation networks, it is crucial to optimize reciprocity among partnering enterprises. However, the impact of psychological distance on subgroup reciprocity in such networks has not yet been investigated. To address this gap, the current study drew on theories of faultlines and cohesive subgroups to model the relationship between psychological distance and subgroup reciprocity within technological innovation networks. Our hypotheses were tested using data from 174 respondents working in Yunnan Province, China. (...) The results were as follows: first, psychological distance had negative effects on subgroup reciprocity in technological innovation networks; second, relationship-divisive and innovation-divisive faultlines negatively impacted reciprocity within and between subgroups; third, the faultlines partially mediated the negative relationship between psychological distance and intra-subgroup reciprocity; and fourth, the negative relationship between psychological distance and subgroup reciprocity was not mediated by the faultlines. The findings uncover the psychological mechanism of subgroup reciprocity within technological innovation networks. They will inform the decision-making process of enterprises when selecting partners within their technological innovation networks and support the development of effective reciprocal relationships with other innovators. (shrink)

By recent work on some conjectures of Pillay, each definably compact group G in a saturated o-minimal expansion of an ordered field has a normal "infinitesimal subgroup" G00 such that the quotient G/G00, equipped with the "logic topology", is a compact (real) Lie group. Our first result is that the functor G → G/G00 sends exact sequences of definably compact groups into exact sequences of Lie groups. We then study the connections between the Lie group G/G00 and the o-minimal (...) spectrum G̃ of G. We prove that G/G00 is a topological quotient of G̃. We thus obtain a natural homomorphism ψ* from the cohomology of G/G00 to the (Čech-)cohomology of G̃. We show that if G00 satisfies a suitable contractibility conjecture then $\widetilde{G^{00}}$ is acyclic in Čech cohomology and ψ* is an isomorphism. Finally we prove the conjecture in some special cases. (shrink)

We show that the stabilizer of an element a of a countable recursively saturated model of arithmetic M is a maximal subgroup of Aut iff the type of a is selective. This is a point of departure for a more detailed study of the relationship between pointwise and setwise stabilizers of certain subsets of M and the types of elements in those subsets. We also show that a complete type of PA is 2-indiscernible iff it is minimal in the (...) sense of Gaifman. (shrink)

A characterization of groups definable in o-minimal structures having maximal definable definably compact subgroups is given. This follows from a definable decomposition in analogy with Lie groups, where the role of maximal tori is played by maximal 0-subgroups. Along the way we give structural theorems for solvable groups, linear groups, and extensions of definably compact by torsion-free definable groups.

In clinical trials, it is common practice to follow up significant interactions between the factors under investigation with subgroup analyses. Such analyses pose at least two analytical and interpretational challenges. The first challenge is that performing multiple subgroup analyses increases the likelihood of obtaining spuriously significant results. This has been acknowledged and relevant guidance exists in the medical literature. The second challenge is that the effects that are obtained at the level of subgroup are composite. This has (...) yet to be fully acknowledged and discussed in the context of medical research. This paper aims to fill this lacuna. Using a simple additive model, we use recent findings from the CHARISMA trial on the efficacy of clopidogrel in addition to aspirin in the treatment of patients at risk for atherothrombotic events to demonstrate quantitatively the composition of effects at the level of subgroups. In the simplest case of a design involving an interaction (two crossed factors, with two levels each, i.e. a 2 x 2 design), effects at the level of subgroup consist of influences that stem (i) from the incidence of the measured outcome in the study population as a whole; (ii) from the factor of interest (e.g. treatment vs. placebo); (iii) from the second factor (e.g. patient group membership); (iv) from the interaction between the two factors; and (v) from random error in the measured outcome. The value of the approach illustrated here is that it is generalizable to any research design irrespective of its complexity and that it prompts clinicians to consider the multiple causality underlying medical research findings. (shrink)

The following theorems are proved about the Frattini-free componentG Φ of a soluble stable ℜ-group: a) If it has a normal subgroupN with nilpotent quotientG Φ/N, then there is a nilpotent subgroupH ofG Φ withG Φ=NH. b) It has Carter subgroups; if the group is small, they are all conjugate. c) Nilpotency modulo a suitable Frattini-subgroup (to be defined) implies nilpotency. The last result makes use of a new structure theorem for the centre of the derivative of the Frattini-free (...) component of a centreless soluble ℜ-group. (shrink)

We prove the following instance of a conjecture stated in [P. E. Eleftheriou and Y. Peterzil, Definable quotients of locally definable groups, Selecta Math. 18 885–903]. Let [Formula: see text] be an abelian semialgebraic group over a real closed field [Formula: see text] and let [Formula: see text] be a semialgebraic subset of [Formula: see text]. Then the group generated by [Formula: see text] contains a generic set and, if connected, it is divisible. More generally, the same result holds when (...) [Formula: see text] is definable in any o-minimal expansion of [Formula: see text] which is elementarily equivalent to [Formula: see text]. We observe that the above statement is equivalent to saying: there exists an [Formula: see text] such that [Formula: see text] is an approximate subgroup of [Formula: see text]. (shrink)

We define a characteristic and definable subgroup F*(G) of any group G of finite Morley rank that behaves very much like the generalized Fitting subgroup of a finite group. We also prove that semisimple subnormal subgroups of G are all definable and that there are finitely many of them.

It is proved that there is a formula$\pi \left$in the first-order language of group theory such that each component and each non-abelian minimal normal subgroup of a finite groupGis definable by$\pi \left$for a suitable elementhofG; in other words, each such subgroup has the form$\left\{ {x|x\pi \left} \right\}$for someh. A number of consequences for infinite models of the theory of finite groups are described.

In this note we treat maximal and minimal normal subgroups of a superstable group and prove that these groups are definable under certain conditions. Main tool is a superstable version of Zil'ber's indecomposability theorem.

Let $\mathcal{M}$ be an o-minimal expansion of a real closed field $R$. We define the notion of a lattice in a locally definable group and then prove that every connected, definably generated subgroup of $\langle R^{n},+\rangle$ contains a definable generic set and therefore admits a lattice.

We generalize two of our previous results on abelian definable groups in p-adically closed fields [12, 13] to the non-abelian case. First, we show that if G is a definable group that is not definably compact, then G has a one-dimensional definable subgroup which is not definably compact. This is a p-adic analogue of the Peterzil–Steinhorn theorem for o-minimal theories [16]. Second, we show that if G is a group definable over the standard model $\mathbb {Q}_p$, then $G^0 = (...) G^{00}$. As an application, definably amenable groups over $\mathbb {Q}_p$ are open subgroups of algebraic groups, up to finite factors. We also prove that $G^0 = G^{00}$ when G is a definable subgroup of a linear algebraic group, over any model. (shrink)

Let $M$ be a saturated model of a superstable theory and let $G = \operatorname{Aut}(M)$. We study subgroups $H$ of $G$ which contain $G_{(A)}, A$ the algebraic closure of a finite set, generalizing results of Lascar [L] as well as giving an alternative characterization of the simple superstable theories of [P]. We also make some observations about good, locally modular regular types $p$ in the context of $p$-simple types.

Given two structures${\cal M}$and${\cal N}$on the same domain, we say that${\cal N}$is a reduct of${\cal M}$if all$\emptyset$-definable relations of${\cal N}$are$\emptyset$-definable in${\cal M}$. In this article the reducts of the Henson digraphs are classified. Henson digraphs are homogeneous countable digraphs that omit some set of finite tournaments. As the Henson digraphs are${\aleph _0}$-categorical, determining their reducts is equivalent to determining the closed supergroupsG≤ Sym of their automorphism groups.A consequence of the classification is that there are${2^{{\aleph _0}}}$pairwise noninterdefinable Henson digraphs which have (...) no proper nontrivial reducts. Taking their automorphisms groups gives a positive answer to a question of Macpherson that asked if there are${2^{{\aleph _0}}}$pairwise nonconjugate maximal-closed subgroups of Sym. By the reconstruction results of Rubin, these groups are also nonisomorphic as abstract groups. (shrink)

Diversity and psychological health issues at the workplace are pressing issues in today’s organizations. However, research linking the two fields is scant. To bridge this gap, drawing from team faultline research, social categorization theory, and the job-demands resources model, we propose that perceiving one’s team as fragmented into subgroups increases strain. We further argue that this relationship is mediated by task conflict and relationship conflict and that it is moderated by psychological empowerment and task interdependence. Multilevel structural equation models on (...) a two-wave sample consisting of 536 participants from 107 work teams across various industries and work contexts partially supported the hypotheses: Task conflict did indeed mediate the positive relationships between perceived subgroups and emotional exhaustion while relationship conflict did not; effects on stress symptoms were absent. Moreover, contrary to our expectations, neither empowerment, nor task interdependence moderated the mediation. Results indicate that team diversity can constitute a job demand that can affect psychological health. Focusing on the mediating role of task conflict, we offer a preliminary process model to guide future research at the crossroads of diversity and psychological health at work. (shrink)

In this paper we discuss automorphism groups of saturated models and boundedly saturated models of $\mathsf{PA}$. We show that there are saturated models of $\mathsf{PA}$ of the same cardinality with nonisomorphic automorphism groups. We then show that every saturated model of $\mathsf{PA}$ has short saturated elementary cuts with nonisomorphic automorphism groups.

The purpose of the present study was to profile high school students’ achievement as a function of their demographic characteristics, parent attributes, and school behaviors. Students were nested within schools in the Saudi Arabia Kingdom. Out of a large sample of 500k, participants involved 3 random samples of 2,000 students measured during the years 2016, 2017, and 2018. Randomization was conducted at the student level to ensure that all school units will be represented and at their respective frequency. Students were (...) nested within 50 high schools. We adopted the multilevel latent profile analysis protocol put forth by Schmiege et al. and Mäkikangas et al. that account for nested data and tested latent class structure invariance over time. Results pointed to the presence of a 4-profile solution based on BIC, the Bayes factor, and several information criteria put forth by Masyn. Latent profile separation was mostly guided by parents’ education and the number of student absences. Two models tested whether the proportions of level 1 profiles to level 2 units are variable and whether level 2 profiles vary as a function of level 1 profiles. Results pointed to the presence of significant variability due to schools. (shrink)

Some first-order theories of divisible ℓ-groups are well known, for example the theory of the totally ordered ones and the theories of the projectable ones , Lattice-ordered Groups, Kluwer Academic Press, Dordrecht, 1989, pp. 41–79). In this paper we study some theories of nonprojectable divisible ℓ-groups, the simplest example of which is . We introduce a generalization of the projectability property . We prove that the class of r-projectable special-valued divisible ℓ-groups is an elementary class and give a classification of (...) its completions. (shrink)

Continuing the earlier research in [1] and [4] we work out a class of interstices in countable arithmetically saturated models of PA in which selective types are realized and a class of interstices in which 2-indiscernible types are realized.

In this paper, I examine Max Deutsch’s dilemma for the implementation of newly engineered concepts. In the debate over this dilemma, the goal of conceptual engineering tends to be set either too high or too low. As a result, implementation tends to be seen as either very unlikely to succeed or too easily achievable. This paper aims to offer a way out of this dilemma. I argue that the success conditions for implementation can be better understood if we distinguish between (...) different stages in the implementation process. Implementation is a complex process involving several stages, each of which can be evaluated as a success or a failure. I argue that even if an implementation does not reach the final stage in which a new concept is widely used in the society at large, it may not be a complete failure: conceptual engineers may not even aim for a new concept to be widely used in the society at large; or even if they do and a new concept only circulates in a smaller subgroup, this can still be a significant achievement. The upshot is that we should take more seriously the possibility that conceptual engineering can be implemented locally at the subgroup level. (shrink)

Let A be an abelian variety in an algebraically closed field of characteristic 0. We prove that the expansion of A by a generic divisible subgroup of A with the same torsion exists provided A has few algebraic endomorphisms, namely. The resulting theory is NSOP1 and not simple. Note that there exist abelian varieties A with of any genus.