Annals of Pure and Applied Logic 89 (1):85-92 (1997)

In this paper, we shall survey results about the group-theoretic properties of stable groups. These can be classified into three main categories, according to the strength of the assumptions needed: chain conditions, generic types, and some form of rank. Each category has its typical application: Chain conditions often allow us to deduce global properties from local ones, generic properties are used to get definable groups from undefinable ones, and rank is necessary to interpret fields in certain group actions. While originally the main input came from algebraic group theory, founded on the similarities between rank and dimension, increasingly methods borrowed from finite group theory have come to play a rôle, emphasizing the study of characteristic subgroups and characteristic families of subgroups
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/s0168-0072(97)00004-3
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 71,512
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

A New Strongly Minimal Set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
Unidimensional Theories Are Superstable.Ehud Hrushovski - 1990 - Annals of Pure and Applied Logic 50 (2):117-137.
Superstable Groups.Ch Berline & D. Lascar - 1986 - Annals of Pure and Applied Logic 30 (1):1-43.
Minimale Gruppen.Joachim Reineke - 1975 - Mathematical Logic Quarterly 21 (1):357-359.
Stability of Nilpotent Groups of Class 2 and Prime Exponent.Alan H. Mekler - 1981 - Journal of Symbolic Logic 46 (4):781-788.

View all 15 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Small Stable Groups and Generics.Frank O. Wagner - 1991 - Journal of Symbolic Logic 56 (3):1026-1037.
Subgroups of Stable Groups.Frank Wagner - 1990 - Journal of Symbolic Logic 55 (1):151-156.
CM-Triviality and Stable Groups.Frank O. Wagner - 1998 - Journal of Symbolic Logic 63 (4):1473-1495.
Simple Stable Homogeneous Groups.Alexander Berenstein - 2003 - Journal of Symbolic Logic 68 (4):1145-1162.
Topological Dynamics and Definable Groups.Anand Pillay - 2013 - Journal of Symbolic Logic 78 (2):657-666.
A Note on Defining Groups in Stable Structures.Frank O. Wagner - 1994 - Journal of Symbolic Logic 59 (2):575-578.
Commutator Conditions and Splitting Automorphisms for Stable Groups.Frank O. Wagner - 1993 - Archive for Mathematical Logic 32 (3):223-228.
On Stable Torsion-Free Nilpotent Groups.Claus Grünenwald & Frieder Haug - 1993 - Archive for Mathematical Logic 32 (6):451-462.
Some Local Properties of Ω-Stable Groups.Katsumi Tanaka - 1988 - Archive for Mathematical Logic 27 (1):45-47.
Nilpotent Complements and Carter Subgroups in Stable ℜ-Groups.Frank O. Wagner - 1994 - Archive for Mathematical Logic 33 (1):23-34.
What Are Groups?Katherine Ritchie - 2013 - Philosophical Studies 166 (2):257-272.
Stable Groups, Mostly of Finite Exponent.Frank O. Wagner - 1993 - Notre Dame Journal of Formal Logic 34 (2):183-192.
Sous-Groupes Periodiques d'Un Groupe Stable.Bruno Poizat & Frank Wagner - 1993 - Journal of Symbolic Logic 58 (2):385-400.


Added to PP index

Total views
11 ( #856,361 of 2,520,896 )

Recent downloads (6 months)
1 ( #405,457 of 2,520,896 )

How can I increase my downloads?


My notes