Archiv der Mathematik

, Volume 102, Issue 2, pp 109–111 | Cite as

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

Article

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).

Mathematics Subject Classification (2010)

20D10 20D20 

Keywords

Finite group Soluble group Hall subgroups 

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References

  1. 1.
    B. Huppert, Endliche Gruppen I, volume 134 of Grund. Math. Wiss. Springer Verlag, Berlin, Heidelberg, New York, 1967.Google Scholar
  2. 2.
    Li S., Liu J.: On Hall subnormally embedded and generalized nilpotent groups. J. Algebra 388, 7–9 (2013)CrossRefGoogle Scholar

Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of MathematicsGuangdong University of EducationGuangzhouPeople’s Republic of China
  2. 2.Departament d’ÀlgebraUniversitat de ValènciaBurjassotSpain
  3. 3.School of Applied MathematicsGuangdong University of TechnologyGuangzhouPeople’s Republic of China

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