Odd order products of conjugate involutions in linear groups over GF(2𝑎)
| Autor: | Peter Rowley, John J. Ballantyne |
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| Rok vydání: | 2021 |
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| Zdroj: | Journal of Group Theory. 24:835-856 |
| ISSN: | 1435-4446 1433-5883 |
| Popis: | Let G be isomorphic to GL n ( q ) {\mathrm{GL}_{n}(q)} , SL n ( q ) {\mathrm{SL}_{n}(q)} , PGL n ( q ) {\mathrm{PGL}_{n}(q)} or PSL n ( q ) {\mathrm{PSL}_{n}(q)} , where q = 2 a {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. |
| Databáze: | OpenAIRE |
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