Cardinal invariants of infinite groups

Archive for Mathematical Logic 30 (3):155-170 (1990)
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Abstract

LetG be a group. CallG akC-group if every element ofG has less thank conjugates. Denote byP(G) the least cardinalk such that any subset ofG of sizek contains two elements which commute.It is shown that the existence of groupsG such thatP(G) is a singular cardinal is consistent withZFC. So is the existence of groupsG which are notkC but haveP(G)

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10.1007/bf01621468

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References found in this work

Classification Theory and the Number of Nonisomorphic Models.S. Shelah - 1982 - Journal of Symbolic Logic 47 (3):694-696.
Basic Set Theory.William Mitchell - 1981 - Journal of Symbolic Logic 46 (2):417-419.
Extraspecial p-groups.Saharon Shelah & Juris Steprāns - 1987 - Annals of Pure and Applied Logic 34 (1):87-97.
Book Review. Basic Set Theory. Azriel Levy. [REVIEW]Harold T. Hodes - 1981 - Philosophical Review 90 (2):298-300.

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