Commuting Involution Graphs of Certain Finite Simple Classical Groups

Everett, Alistaire (2011) Commuting Involution Graphs of Certain Finite Simple Classical Groups. Doctoral thesis, Manchester Institute for Mathematical Sciences, The University of Manchester.

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For a group G and X a subset of G, the commuting graph of G on X, denoted by C(G,X), is the graph whose vertex set is X with x, y in X joined by an edge if x is not equal to y and x and y commute. If the elements in X are involutions, then C(G,X) is called a commuting involution graph. This thesis studies C(G,X) when G is either a 4-dimensional projective symplectic group; a 3-dimensional unitary group; 4-dimensional unitary group over a field of characteristic 2; a 2-dimensional projective general linear group; or a 4-dimensional affine orthogonal group, and X a G-conjugacy class of involutions. We determine the diameters and structure of the discs of these graphs.

Item Type: Thesis (Doctoral)
Uncontrolled Keywords: Commuting Involution Graphs, Involutions, Symplectic Groups, Unitary Groups, Affine Orthogonal Groups, Projective General Linear Groups
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
Depositing User: Mr Alistaire Everett
Date Deposited: 29 Jun 2011
Last Modified: 20 Oct 2017 14:12

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