Skip to main content
SpringerLink
Log in

Local Subgroups and Group Algebras of Finite p-Solvable Groups

  • Published:
Algebras and Representation Aims and scope Submit manuscript

Abstract

Let p be a prime, k an algebraically closed field ofcharacteristic p, and G a finite group with a Sylowp-Subgroup P. In this paper, we consider the property thatNG(P)/P is Abelian. We provide somenecessary or sufficient conditions NG(P)/P to be Abelian in term of thestructure of the group algebra kG as a k-algebra, in casethat G is p-nilpotent or of p-length 1.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aschbacher, M.: Finite Group Theory, Cambridge Univ. Press, Cambridge, 1986.

    Google Scholar 

  2. Hamernik, W. and Michler, G.: On vertices of simple modules in p-solvable groups, Mitt. Math. Sem. Giessen 121(1976), 147–162.

    Google Scholar 

  3. Isaacs, I. M.: Character Theory of Finite Groups, Dover, New York, 1994.

  4. Michler, G. O.: A finite simple group of Lie type has p-block with different defects, p≠ 2, J. Algebra 104(1986), 220–230.

    Google Scholar 

  5. Morita, K.: On group rings over a modular field which possess radicals expressible as principal ideals, Sci. Rep. Tokyo Bunrika Daigaku. Sec. A 4(1951), 177–194.

    Google Scholar 

  6. Nagao, H. and Tsushima, Y.: Representations of Finite Groups, Academic Press, New York, 1989.

    Google Scholar 

  7. Navarro, G.: Two groups with isomorphic group algebras, Arch. Math. 55(1990), 35–37.

    Google Scholar 

  8. Okuyama, T.: Module correspondence in finite groups, Hokkaido J. Math. 10(1981), 299–318.

    Google Scholar 

  9. Okuyama, T.: On a problem of Wallace, unpublished.

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering, Yamanashi University, Kofu, 400, Japan

    Akihide Hanaki

  2. Department of Mathematics, Chiba University, Chiba, 263, Japan

    Shigeo Koshitani

Authors
  1. Akihide Hanaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shigeo Koshitani
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hanaki, A., Koshitani, S. Local Subgroups and Group Algebras of Finite p-Solvable Groups. Algebras and Representation Theory 1, 155–159 (1998). https://doi.org/10.1023/A:1009937601589

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009937601589

Search

Navigation