Chinese Annals of Mathematics, Series B

, Volume 40, Issue 4, pp 613–642 | Cite as

The Automorphism Group of a Finite p-Group with a Cyclic Frattini Subgroup

  • Heguo LiuEmail author
  • Yulei WangEmail author


Let G be a finite p-group with a cyclic Frattini subgroup. In this paper, the automorphism group of G is determined.


Finite p-groups Frattini subgroups Automorphisms 

2000 MR Subject Classification



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Robinson, D. J. S., A Course in the Theory of Groups, 2nd ed., Springer-Verlag, New York, 1996.CrossRefGoogle Scholar
  2. [2]
    Winter, D., The automorphism group of an extraspecial p-group, Rocky Mountain J. Math., 2, 1972, 159–168.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Dietz, J., Automorphisms of p-group given as cyclic-by-elementary abelian central extensions, J. Algebra, 242, 2001, 417–432.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Liu, H. G. and Wang, Y. L., The automorphism group of a generalized extraspecial p-group, Sci. China Math., 53(2), 2010, 315–334.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Wang, Y. L. and Liu, H. G., Generalization of Winter’s theorem and Dietz’s theorem, Chin. J. Contemp. Math., 33(4), 2012, 375–394.MathSciNetzbMATHGoogle Scholar
  6. [6]
    Bornand, D., Elementary abelian subgroups in p-groups of class 2, École Polytechnique Fédérale de lausanne, Lausanne, 2009.zbMATHGoogle Scholar

Copyright information

© The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2019

Authors and Affiliations

  1. 1.Department of MathematicsHubei UniversityWuhanChina
  2. 2.Department of MathematicsHenan University of TechnologyZhengzhouChina

Personalised recommendations