Ballantyne, John and Rowley, Peter
(2016)
*Odd Order Products of Conjugate Involutions in Linear Groups over GF(2^a).*
[MIMS Preprint]

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## Abstract

Let $G$ be isomorphic to $GL_n(q)$, $SL_n(q)$, $PGL_n(q)$ or $PSL_n(q)$, where $q=2^a$. If $t$ is an involution lying in a $G$-conjugacy class $X$, then for arbitrary $n$ we show that as $q$ becomes large, the proportion of elements of $X$ which have odd-order product with $t$ tends to $1$. Furthermore, for $n$ at most $4$ we give formulae for the number of elements in $X$ which have odd-order product with $t$, in terms of $q$.

Item Type: | MIMS Preprint |
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Uncontrolled Keywords: | involution; linear groups; odd order |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations |

Depositing User: | Dr John Ballantyne |

Date Deposited: | 26 Jul 2016 |

Last Modified: | 08 Nov 2017 18:18 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/2487 |

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