Odd Order Products of Conjugate Involutions in Linear Groups over GF(2^a)

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

[thumbnail of SL_nPaper230315.pdf] PDF
SL_nPaper230315.pdf

Download (335kB)

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
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: https://eprints.maths.manchester.ac.uk/id/eprint/2487

Actions (login required)

View Item View Item