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2011.23: Commuting Involution Graphs of Certain Finite Simple Classical Groups

2011.23: Alistaire Everett (2011) Commuting Involution Graphs of Certain Finite Simple Classical Groups. PhD 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 (PhD)
Uncontrolled Keywords:Commuting Involution Graphs, Involutions, Symplectic Groups, Unitary Groups, Affine Orthogonal Groups, Projective General Linear Groups
Subjects:MSC 2000 > 20 Group theory and generalizations
MIMS number:2011.23
Deposited By:Mr Alistaire Everett
Deposited On:29 June 2011

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