Archiv der Mathematik

, Volume 73, Issue 1, pp 11–14 | Cite as

On self-normality and abnormality in the alternating group Ap

  • Qinhai Zhang


An old problem proposed by Huppert, Doerk and Hawkes motivates us to investigate the relationship between an abnormal subgroup and self-normalizing in non-solvable groups. A subgroup H of a group G is called second maximal if H is maximal in all maximal subgroups of G containing H. Our result is that if H is a second maximal subgroup of the alternating group Ap of prime degree, then H is abnormal in Ap if and only if H is self-normalizing.


Maximal Subgroup Prime Degree Abnormal Subgroup 


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Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • Qinhai Zhang
    • 1
  1. 1.Mathematical Department, Shanxi Teachers University, Linfen, Shanxi 041004, P.R. ChinaChina

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