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

The following paper has been published.

El siguiente artículo ha sido publicado.

El següent article ha sigut publicat.

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.

The following paper has been accepted for publication.

El siguiente artículo ha sido aceptado para su publicación.

El següent article ha sigut acceptat per ser publicat.

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