Conjugacy classes in parabolic subgroups of general linear groups
نویسندگان
چکیده
منابع مشابه
Conjugacy Classes in Maximal Parabolic Subgroups of General Linear Groups
We compute conjugacy classes in maximal parabolic subgroups of the general linear group. This computation proceeds by reducing to a “matrix problem”. Such problems involve finding normal forms for matrices under a specified set of row and column operations. We solve the relevant matrix problem in small dimensional cases. This gives us all conjugacy classes in maximal parabolic subgroups over a ...
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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 GLn(q). We show that the number of P (q)conjugacy classes in GLn(q) is, as a function of q, a polynomial in q with integer coefficients. This answers a question of J. Alperin in [1].
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Let $G$ be a finite group and $nu(G)$ denote the number of conjugacy classes of non-normal subgroups of $G$. In this paper, all nilpotent groups $G$ with $nu(G)=3$ are classified.
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We prove the properties of induced conjugacy classes, without using the original proof by Lusztig and Spaltenstein in the unipotent case, by adapting Borho’s simpler arguments for induced adjoint orbits. We study properties of equivariant fibrations of prehomogeneous affine spaces, especially the existence of relative invariants. We also detect prehomogeneous affine spaces as subquotients of ca...
متن کاملnilpotent groups with three conjugacy classes of non-normal subgroups
let $g$ be a finite group and $nu(g)$ denote the number of conjugacy classes of non-normal subgroups of $g$. in this paper, all nilpotent groups $g$ with $nu(g)=3$ are classified.
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2009
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgt.2008.058