A NOTE ON THE p-NILPOTENCY OF A FINITE GROUP

Year 2012, Volume: 11 Issue: 11, 12 - 19, 01.06.2012

Changwen Li

Abstract

Suppose that G is a finite group and H is a subgroup of G. H
is said to be s-quasinormally embedded in G if for each prime p dividing |H|,
a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-quasinormal
subgroup of G; H is called weakly s-supplemented in G if there is a subgroup
T of G such that G = HT and H ∩ T ≤ HsG, where HsG is the subgroup of H
generated by all those subgroups of H which are s-quasinormal in G. We investigate
the influence of s-quasinormally embedded and weakly s-supplemented
subgroups on the p-nilpotency of a finite group.

Keywords

s-quasinormally embedded, weakly s-supplemented, p-nilpotent, 2-maximal subgroup

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• School of Mathematical Science Xuzhou Normal University Xuzhou, 221116
• People’s Republic of China e-mail: [e-mail]