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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:570298 |
| Date | January 2013 |
| Creators | Nawawi, Athirah Binti |
| Contributors | Walker, Louise; Rowley, Peter |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://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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