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Sylow subgroups of groups with Černikov conjugacy classes. (English) Zbl 0624.20026

It is well known that the Sylow \(p\)-subgroups (i.e. maximal p-subgroups) of an FC-group are locally conjugate. The authors extend this result to groups with Chernikov classes, that is groups \(G\) in which \(G/C_ G(x^ G)\) is a Chernikov group for each \(x\in G\). For FC-groups the result depends on the inverse limit of finite non-empty sets being non-empty. For CC-groups the stronger result that the inverse limit of non-empty compact \(T_ 1\)-spaces is non-empty is required. It is also shown that the Sylow \(p\)-subgroups are conjugate if and only if there are only countably many of them.
Reviewer: M.J.Tomkinson

MSC:

20F24 FC-groups and their generalizations
20E07 Subgroup theorems; subgroup growth
20E25 Local properties of groups
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References:

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