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On periodic radical groups in which permutability is a transitive relation. (English) Zbl 1119.20044

A group \(G\) is called radical, if every nontrivial quotient group of \(G\) has a nontrivial Hirsch-Plotkin radical. The authors consider periodic radical groups \(G\) with minimum condition for \(p\)-groups and transitivity for permutability.
Main results: \(G\) is metabelian and its Hirsch-Plotkin radical is the direct product of the locally nilpotent residual and the upper hypercenter of \(G\) (Theorems 3 and 4).

MSC:

20F50 Periodic groups; locally finite groups
20E15 Chains and lattices of subgroups, subnormal subgroups
20E07 Subgroup theorems; subgroup growth
20E22 Extensions, wreath products, and other compositions of groups
20F19 Generalizations of solvable and nilpotent groups
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References:

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