Perfect locally finite groups that are product of normal soluble subgroups of bounded derived length (Q6601217)

Let \(G\) be a group and let \(\mathfrak{X}\) be a class of groups. If \(G \not \in \mathfrak{X}\) but \(H \in \mathfrak{X}\) for every \(H \lvertneqq G\), then \(G\) is called \(MN\mathfrak{X}\)-group (minimal non-\(\mathfrak{X}\)-group).\N\NIn the paper under review, authors consider infinite locally finite perfect groups that are product of proper normal soluble subgroups of derived length at most \(n\) for some fixed positive integer \(n\) (that they call \(\Pi \mathfrak{S}_{n}\)-groups) and give structural results for these groups. They also provide some consequences for certain locally finite \(MN\mathfrak{X}\)-groups for some classes \(\mathfrak{X}\) (in particular hypercentral, FC and soluble groups). Furthermore, they define certain collections of groups and consider their intersection with the class \(\Pi \mathfrak{S}_{n}\).