Commuting Involution Graphs of Certain Finite Simple Classical Groups

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 joined by an edge if x 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 affne orthogonal group, and X a G-conjugacy class of involutions. We determine the diameters and structure of thediscs of these graphs.

Date of Award	1 Aug 2011
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Peter Rowley (Supervisor) & Charles Eaton (Supervisor)