Elkholy, A. M.; Abd-Ellatif, M. H. Finite groups with certain S-permutable and GS-maximal subgroups. (English) Zbl 1506.20015 Algebra Colloq. 27, No. 4, 661-668 (2020). 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 Keywords:smooth groups; subgroup lattices; S-permutability PDFBibTeX XMLCite \textit{A. M. Elkholy} and \textit{M. H. Abd-Ellatif}, Algebra Colloq. 27, No. 4, 661--668 (2020; Zbl 1506.20015) Full Text: DOI