On periodic radical groups in which permutability is a transitive relation. (Q886255)

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).