Minimal normal subgroups of dinilpotent groups
A group \(G\) is said to be dinilpotent if it has a nilpotent factorization, i.e., if \(G=AB\), where \(A\) and \(B\) are nilpotent subgroups of \(G\). It was proved by \textit{S. E. Stonehewer} [J. Pure Appl. Algebra 88, No. 1-3, 239-244 (1993; Zbl 0784.20012)] that if \(N\) is a minimal normal subgroup of a finite dinilpotent group \(G=AB\), then at least one of the subgroups \(AN\) and \(BN\) is nilpotent. In this article the authors extend this result to several classes of infinite groups. In particular, they show that if the dinilpotent group \(G=AB\) is nilpotent-by-polycyclic and \(A\cap B\) is periodic, then either \(AN\) or \(BN\) is nilpotent for every minimal normal subgroup \(N\) of \(G\). Some consequences of this theorem are also proved.
scientific article; zbMATH DE number 1565870
scientific article