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 |
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Pages (from-to) | 55-66 |
Number of pages | 12 |
Journal | Geometriae Dedicata |
Volume | 88 |
Issue number | 1-3 |
DOIs | |
State | Published - 1 Dec 2001 |
Keywords
- Commuting graph
- Division algebra
- Minimal nonsolvable
- Partitions
ASJC Scopus subject areas
- Geometry and Topology