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Acta Mathematica Vietnamica

A NOTE ON WEAKLY s-PERMUTABLY EMBEDDED AND WEAKLY s-SUPPLEMENTED SUBGROUPS

icon-email CHANGWEN LI

Abstract

Suppose that G is a finite group and H is a subgroup of G. H is called weakly s-permutably embedded in G if there are a subnormal subgroup T of G and an s-permutably embedded subgroup Hse of G contained in H such that G=HT and HTHse; H is called weakly s-supplemented in G if there is a subgroup T of G such that G=HT and HTHsG, where HsG is the subgroup of H generated by all those subgroups of H which are s-permutable in G. We investigate the influence of weakly s-permutably embedded and weakly s-supplemented subgroups on the p-nilpotency of finite groups. Some recent results are generalized.