On locally finite groups factorized by locally nilpotent subgroups
The authors extend some well-known facts about finite products of two nilpotent subgroups to periodic radical groups \(G=AB\) which are the product of two locally nilpotent subgroups \(A\) and \(B\). For instance, it is shown that if \(A\) or \(B\) is hyperabelian and \(N\) is a minimal normal subgroup of \(G\), then one of the subgroups \(AN\) or \(BN\) is locally nilpotent. If \(A\) and \(B\) are nilpotent of classes \(c\) and \(d\), then the \((c+d+1)\)-th term of the derived series of \(G\) is locally nilpotent. If the periodic radical group \(G=AB=AC=BC\) is the product of three locally nilpotent subgroups \(A\), \(B\) and \(C\), at least one of which is hyperabelian, then \(G\) is locally nilpotent. The proofs of these results do not use that they are already known in the finite case [see the book ``Products of groups'' (1992; Zbl 0774.20001) by the first two authors and the reviewer].
scientific article; zbMATH DE number 858631
scientific article