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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Abstract
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) |
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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: | 02 Mar 2011 |
Last Modified: | 20 Oct 2017 14:12 |
URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1581 |
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