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).
| Original language | English |
|---|---|
| Pages (from-to) | 99-111 |
| Number of pages | 13 |
| Journal | Journal of Algebraic Combinatorics |
| Volume | 27 |
| Issue number | 1 |
| Early online date | 15 Jun 2007 |
| DOIs | |
| Publication status | Published - 1 Feb 2008 |
Keywords
- parabolic subgroups
- conjugacy classes
- general linear group