The Commuting Graph of Minimal Nonsolvable Groups

Yoav Segev

doi:10.1023/A:1013180005982

The Commuting Graph of Minimal Nonsolvable Groups

Yoav Segev

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

49 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 language	English
Pages (from-to)	55-66
Number of pages	12
Journal	Geometriae Dedicata
Volume	88
Issue number	1-3
DOIs	https://doi.org/10.1023/A:1013180005982
State	Published - 1 Dec 2001

Keywords

Commuting graph
Division algebra
Minimal nonsolvable
Partitions

ASJC Scopus subject areas

Geometry and Topology

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10.1023/A:1013180005982

Cite this

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AB - 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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KW - Partitions

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The Commuting Graph of Minimal Nonsolvable Groups

Abstract

Keywords

ASJC Scopus subject areas

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