Geodesic
Parabolic conjugacy in general linear groups.
Journal of Algebraic Combinatorics, Tome 27 (2008) no. 1, pp. 99-111.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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)
Keywords: keywords general linear group, parabolic subgroups, conjugacy classes 
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     title = {Parabolic conjugacy in general linear groups.},
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Goodwin, Simon M.; Röhrle, Gerhard. Parabolic conjugacy in general linear groups.. Journal of Algebraic Combinatorics, Tome 27 (2008) no. 1, pp. 99-111. http://geodesic.mathdoc.fr/item/JAC_2008__27_1_a1/