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The Commuting Graph of Minimal Nonsolvable Groups

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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.

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Authors and Affiliations

  1. Department of Mathematics, Ben-Gurion University, Beer-Sheva, 84105, Israel

    Yoav Segev

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  1. Yoav Segev
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Segev, Y. The Commuting Graph of Minimal Nonsolvable Groups. Geometriae Dedicata 88, 55–66 (2001). https://doi.org/10.1023/A:1013180005982

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