×

Finite groups with certain S-permutable and GS-maximal subgroups. (English) Zbl 1506.20015

Summary: Let \(G\) be a finite group and \(H\) a subgroup of \(G\). We say that \(H\) is S-permutable in \(G\) if \(H\) permutes with every Sylow subgroup of \(G\). A group \(G\) is called a generalized smooth group (GS-group) if \([G/L]\) is totally smooth for every subgroup \(L\) of \(G\) of prime order. In this paper, we investigate the structure of \(G\) under the assumption that each subgroup of prime order is S-permutable if the maximal subgroups of \(G\) are GS-groups.

MSC:

20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
20D30 Series and lattices of subgroups
20D40 Products of subgroups of abstract finite groups
PDFBibTeX XMLCite
Full Text: DOI