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Commuting graphs for elements of order three in finite groups

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.

Identiferoai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:570298
Date January 2013
CreatorsNawawi, Athirah Binti
ContributorsWalker, Louise; Rowley, Peter
PublisherUniversity of Manchester
Source SetsEthos UK
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
Sourcehttps://www.research.manchester.ac.uk/portal/en/theses/commuting-graphs-for-elements-of-order-three-in-finite-groups(40587bc6-4448-4ab2-9a93-ebcd64b2846b).html

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