On hall subnormally embedded subgroups of finite groups

Ballester-Bolinches, Adolfo; Cossey, John; Qiao, Shou Hong

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On hall subnormally embedded subgroups of finite groups

Date

2016-12-01

Authors

Ballester-Bolinches, Adolfo

Cossey, John

Qiao, Shou Hong

Abstract

A subgroup H of a finite group G is said to be Hall subnormally (respectively normally) embedded in G if there is a subnormal (respectively normal) subgroup N of G such that H is a Hall subgroup of N. The aim of this paper is to characterise the groups G having a Hall subnormally embedded subgroup of order |B| for each subgroup B of G. Some earlier results are consequences of our main theorem.