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Commuting Involution Graphs of Certain Finite Simple Classical Groups

Everett, Alistaire Duncan Fraser

[Thesis]. Manchester, UK: The University of Manchester; 2011.

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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 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.

Bibliographic metadata

Type of resource:
Content type:
Form of thesis:
Type of submission:
Degree type:
Doctor of Philosophy
Degree programme:
PhD Mathematical Sciences
Publication date:
Location:
Manchester, UK
Total pages:
154
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.
Thesis main supervisor(s):
Thesis co-supervisor(s):
Thesis advisor(s):
Funder(s):
Language:
en

Institutional metadata

University researcher(s):

Record metadata

Manchester eScholar ID:
uk-ac-man-scw:124672
Created by:
Everett, Alistaire
Created:
20th June, 2011, 11:04:27
Last modified by:
Everett, Alistaire
Last modified:
23rd May, 2012, 18:58:06

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