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Commuting graphs for elements of order three in finite groups
- Publication Year :
- 2013
- Publisher :
- University of Manchester, 2013.
-
Abstract
- Let G be a finite group and X a subset of G. The commuting graph C(G,X) is the graph whose vertex set is X with two distinct elements of X joined by an edge whenever they commute in the group G. This thesis studies the structure of commuting graphs C(G,X) when G is either a symmetric group Sym(n) or a sporadic group McL, and X a conjugacy class for elements of order three. We describe how this graph can be useful in understanding various aspects of the structure of the group with a particular emphasis on the connectivity of the graph, the properties of the discs around some fixed vertex and the diameter of the graph.
- Subjects :
- 512
commuting graph
elements of order three
symmetric group
diameter
connectivity
Subjects
Details
- Language :
- English
- Database :
- British Library EThOS
- Publication Type :
- Dissertation/ Thesis
- Accession number :
- edsble.570298
- Document Type :
- Electronic Thesis or Dissertation