## 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) |
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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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- Commuting Involution Graphs of Certain Finite Simple Classical Groups (deposited 29 June 2011)
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