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Topologically locally finite groups with a CC-subgroup. (English) Zbl 1062.22008

Let \(G\) be a finite group. A proper subgroup \(M\) of \(G\) is called a CC-subgroup of \(G\) if \(C_G(m)\subseteq M\) for every non-identity \(m\in M\). Although a few authors worked on the classification of finite groups having a CC-subgroup, their final classification was obtained by Z. Arad and W. Herfort [Commun. Algebra 32, No. 6, 2087–2098 (2004; Zbl 1070.20023)]. In the paper under review, the authors classify totally disconnected topologically finite groups containing a topological analogue of a CC-subgroup.

MSC:

22D05 General properties and structure of locally compact groups
20E18 Limits, profinite groups
20F50 Periodic groups; locally finite groups

Citations:

Zbl 1070.20023
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