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Adolfo Ballester-Bolinches, John Cossey, and ShouHong Qiao.
On Hall subnormally embedded subgroups of finite groups.
Monatsh. Math., 181(4):753–760, 2016
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.
2010 Mathematical Subject Classification: 20D10 20D20
Keywords: Finite group, Soluble group, Hall subgroup, Subnormal subgroup