Paper “On hall subnormally embedded subgroups of finite groups” published in Monatsh. Math.

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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

https://doi.org/10.1007/s00605-015-0838-0

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.

2010 Mathematical Subject Classification: 20D10 20D20

Keywords: Finite group, Soluble group, Hall subgroup, Subnormal subgroup

Paper “On a problem posed by S. Li and J. Liu” published in Arch. Math.

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Adolfo Ballester-Bolinches, Shouhong Qiao

On a problem posed by S. Li and J. Liu

Arch. Math., 102, 109-111 (2014)

http://dx.doi.org/10.1007/s00013-014-0617-5

Abstract: A subgroup H of a finite group G is said to be Hall normally
embedded in G if there is a normal subgroup N of G such that H is a
Hall subgroup of N . The aim of this note is to prove that a group G has
a Hall normally embedded subgroup of order |B| for each subgroup B of
G if and only if G is soluble with nilpotent residual cyclic of square-free
order. This is the answer to a problem posed by Li and Liu (J. Algebra
388:1–9, 2013).


MSC: 20D10, 20D20
Keywords: Finite group, soluble group, Hall subgroups

Paper “On a paper posed by S. Li and J. Liu” to appear in Arch. Math.

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Adolfo Ballester-Bolinches, Shouhong Qiao

On a problem posed by S. Li and J. Liu

Arch. Math., in press

http://dx.doi.org/10.1007/s00013-014-0617-5

Abstract: A subgroup H of a finite group G is said to be Hall normally
embedded in G if there is a normal subgroup N of G such that H is a
Hall subgroup of N . The aim of this note is to prove that a group G has
a Hall normally embedded subgroup of order |B| for each subgroup B of
G if and only if G is soluble with nilpotent residual cyclic of square-free
order. This is the answer to a problem posed by Li and Liu (J. Algebra
388:1–9, 2013).


MSC: 20D10, 20D20
Keywords: Finite group, soluble group, Hall subgroups