Direct products of inseparable finite groups
A finite group is inseparable if it does not split over any nontrivial proper normal subgroup. Let \(G = S_ 1 \times \cdots\times S_ m\) be a direct product of nontrivial finite inseparable groups, and let \(\{T_ 1,\dots,T_ n\}\) be an ordered set of nontrivial inseparable subgroups of \(G\) such that \(G = T_ 1 \cdots T_ n\) and whenever \(1 \leq i < n\), the product \(T_ 1 \cdots T_ i\) is a subgroup normalized and avoided by \(T_{i+1}\). Then \(n = m\) and there is a permutation \(\pi\) of the set \(\{1,\dots,n\}\) such that \(S_{\pi(j)} \cong T_ j\) for \(j = 1,\dots,n\).
scientific article; zbMATH DE number 563362