The Commuting Graph of Minimal Nonsolvable Groups

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41 Scopus citations

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.

Original languageEnglish
Pages (from-to)55-66
Number of pages12
JournalGeometriae Dedicata
Volume88
Issue number1-3
DOIs
StatePublished - 1 Dec 2001

Keywords

  • Commuting graph
  • Division algebra
  • Minimal nonsolvable
  • Partitions

ASJC Scopus subject areas

  • Geometry and Topology

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