Conjugacy classes in Sylow p-subgroups of GL(n, q)
نویسندگان
چکیده
منابع مشابه
COUNTING CONJUGACY CLASSES IN THE UNIPOTENT RADICAL OF PARABOLIC SUBGROUPS OF GLn(q)
Let q be a power of a prime p. Let P be a parabolic subgroup of the general linear group GLn(q) that is the stabilizer of a flag in F n q of length at most 5, and let U = Op(P ). In this note we prove that, as a function of q, the number k(U) of conjugacy classes of U is a polynomial in q with integer coefficients.
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In [8, §8], the first author outlined an algorithm for calculating a parametrization of the conjugacy classes in a Sylow p-subgroup U(q) of a finite Chevalley group G(q), valid when q is a power of a good prime for G(q). In this paper we develop this algorithm and discuss an implementation in the computer algebra language GAP. Using the resulting computer program we are able to calculate the pa...
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For any conjugacy class C in G = PSL2(q) we compute C and discuss whether C contains a triple of elements whose product is 1 which generate G. Moreover, we determine which elements in G can be written as a product of two conjugate elements that generate G.
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Abstract. Let SL(2, q) be the group of 2× 2 matrices with determinant one over a finite field F of size q. We prove that if q is even, then the product of any two noncentral conjugacy classes of SL(2, q) is the union of at least q − 1 distinct conjugacy classes of SL(2, q). On the other hand, if q > 3 is odd, then the product of any two noncentral conjugacy classes of SL(2, q) is the union of a...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1992
ISSN: 0021-8693
DOI: 10.1016/0021-8693(92)90085-z