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