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manuscripta mathematica

, Volume 41, Issue 1–3, pp 233–305 | Cite as

Auflösbare Gruppen auf denen nicht auflösbare Gruppen operieren

  • Hans Kurzweil
Article

Abstract

Let G be a finite solvable group and A a subgroup of Aut G such that ¦G¦ and ¦A¦ are coprime. A conjecture states: The nilpodent length of G is bounded by terms depending only on A and the fixed point group GA={g∈G¦gA=g}. For abelian, nilpotent or solvable A various bounds are known. In this paper we study the nonsolvable case and prove the conjecture for wide classes of nonsolvable groups A, especially in the fixed point free case GA=1.

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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Hans Kurzweil
    • 1
  1. 1.Mathematisches Institut der Universität Erlangen-NürnbergErlangenW-Germany

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