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Groups with all cyclic subgroups conjugate-permutable groups. (English) Zbl 0921.20035

A group \(G\) is said to be a CCP-group if every cyclic subgroup of \(G\) commutes with all its conjugates. The author proves that, if \(G\) is any CCP-group, then the set \(T(G)\) of all elements of finite order of \(G\) is a locally nilpotent subgroup.

MSC:

20E25 Local properties of groups
20E07 Subgroup theorems; subgroup growth
20F50 Periodic groups; locally finite groups
20D40 Products of subgroups of abstract finite groups
20E22 Extensions, wreath products, and other compositions of groups
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References:

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