Parabolic conjugacy in general linear groups |
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| Authors: | Simon M. Goodwin Gerhard Röhrle |
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| Affiliation: | 1. School of Mathematics, University of Birmingham, Birmingham, B15 2TT, UK
2. Fakult?t für Mathematik, Ruhr-Universit?t Bochum, Universit?tsstrasse 150, 44780, Bochum, Germany
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| Abstract: | Let q be a power of a prime and n a positive integer. Let P(q) be a parabolic subgroup of the finite general linear group GL n (q). We show that the number of P(q)-conjugacy classes in GL n (q) is, as a function of q, a polynomial in q with integer coefficients. This answers a question of Alperin in (Commun. Algebra 34(3): 889–891, 2006) |
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| Keywords: | General linear group Parabolic subgroups Conjugacy classes |
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