Skip to main content
Log in

A result about Abelian automorphism groups

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

Some new techniques are given to prove that two sorts of Abelian groups cannot function as the full automorphism groups of the finite groups. With generality these techniques made a breakthrough in MacHale’s problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Ban Guining, Yu Shuxia. The orders of automorphism groups of somep-groups (p>3),Acta Mathematica Sinica (in Chinese), 1992, 35(4): 570.

    MATH  MathSciNet  Google Scholar 

  2. Ban Guining, Yu Shuxia, A counterexample of Curran’s third conjecture,Advances in Mathematics (in Chinese), 1994, 23 (3): 272.

    MATH  MathSciNet  Google Scholar 

  3. Ban Guining, Solution of Curran’ s conjectures,Advances in Mathematics (in Chinese). 1996, 25(2): 159.

    MATH  MathSciNet  Google Scholar 

  4. Yu Shuxia, Ban Guining, Zhang Jingsong, Minimalp-groups with automorphism groups of orderp 7,Algebra Collq., 1996, 3(2): 97.

    MATH  Google Scholar 

  5. Ying, J. H., On finite groups whose automorphism groups are nilpotent,Arch. Math., 1977, 29: 41.

    Article  MATH  Google Scholar 

  6. Flannery. D., MacHale, D., Some finite groups which are rarely automorphism groups-I.Proc. Roy. Ir. Acad., 1981, 81A(2); 209.

    MathSciNet  Google Scholar 

  7. MacHale, D., Some finite groups which are rarely automorphism - II.Proc. Roy. Ir. Acad., 1983, 83A(2): 189.

    MathSciNet  Google Scholar 

  8. Jonah, D., Konvisser, M., Some non-Abelianp -groups with Abelian automorphism groups,Arch. Math., 1975, 26: 131.

    Article  MATH  MathSciNet  Google Scholar 

  9. Morigi, M., On the minimal number of generators of finite non-Abelianp-groups having an Abelian automorphisrn group,Communications in Algebra, 1995, 23(6): 2045.

    Article  MATH  MathSciNet  Google Scholar 

  10. Davitt, R. M., On the automorphisrn group of finitep-group with a small central quotient,Can. J. Math., 1980, 32(5): 1168.

    MATH  MathSciNet  Google Scholar 

  11. Davitt, R. M., Otto, A. D., On the automorphism group of finitep-group with the central quotient metacyclic,Proc. Amer. Math. Soc., 1971, 30(3): 467.

    Article  MATH  MathSciNet  Google Scholar 

  12. Heineken, H., Liebeck, H., Onp-groups with odd order automorphism groups,Arch. Math., 1973, 24: 465.

    Article  MATH  MathSciNet  Google Scholar 

  13. Huppert, B.,Endliche Gruppen I, New York: Springer-Verlag, 1979.

    MATH  Google Scholar 

  14. Exarchakos, T., LA-groups,J. Math. Soc. Japan, 1981, 33(2): 185.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Project supported by the National Natural Science Foundation of China.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ban, G., Yu, S. A result about Abelian automorphism groups. Sci. China Ser. A-Math. 40, 494–500 (1997). https://doi.org/10.1007/BF02896957

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02896957

Keywords

Navigation