Totally permutable products of certain classes of finite groups. (Q1886835)

Let \(G\) be a finite group. Subgroups \(A\) and \(B\) of \(G\) are said to be totally permutable if every subgroup of \(A\) permutes with every subgroup of \(B\). Let \(G=G_1G_2\cdots G_r\) be the product of finite pairwise totally permutable subgroups \(G_1,\dots,G_r\). In this paper the authors study the relation between \(G\) and \(G_i\), \(i\in\{1,2,\dots,r\}\) and get a series of significant results, for example, \(G\) is an SC-group (all chief factors are simple) if and only if \(G_i\) is an SC-group for all \(i\in\{1,2,\dots,r\}\).