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Odd order products of conjugate involutions in linear groups over GF(2𝑎)
Journal of Group Theory ( IF 0.4 ) Pub Date : 2021-07-01 , DOI: 10.1515/jgth-2020-0120 John J. Ballantyne 1 , Peter J. Rowley 2
Journal of Group Theory ( IF 0.4 ) Pub Date : 2021-07-01 , DOI: 10.1515/jgth-2020-0120 John J. Ballantyne 1 , Peter J. Rowley 2
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Let G be isomorphic to GLn(q){\mathrm{GL}_{n}(q)}, SLn(q){\mathrm{SL}_{n}(q)}, PGLn(q){\mathrm{PGL}_{n}(q)} or PSLn(q){\mathrm{PSL}_{n}(q)}, where q=2a{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 .
更新日期：2021-07-01
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