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Geometriae Dedicata

, Volume 88, Issue 1–3, pp 55–66 | Cite as

The Commuting Graph of Minimal Nonsolvable Groups

  • Yoav Segev
Article

Abstract

The purpose of this paper is to prove that if G is a finite minimal nonsolvable group (i.e. G is not solvable but every proper quotient of G is solvable), then the commuting graph of G has diameter ≥3. We give an example showing that this result is the best possible. This result is related to the structure of finite quotients of the multiplicative group of a finite-dimensional division algebra.

commuting graph minimal nonsolvable partitions division algebra 

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Yoav Segev
    • 1
  1. 1.Department of MathematicsBen-Gurion UniversityBeer-ShevaIsrael

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