On conjugacy classes of p-elements
نویسندگان
چکیده
منابع مشابه
ON THE NUMBER OF CONJUGACY CLASSES OF FINITE p-GROUPS
Denote k(G) the number of conjugacy classes of a group G. Some inequalities are deduced by arithmetic means for k(G), where G is a p-group. As an application, k(G) is calculated for special cases of p-groups. A method of estimating k(G) for some finite groups, others then p-groups is also presented.
متن کاملCONJUGACY CLASSES IN FINITE p-GROUPS
Of course, in that problem we have to take into account that the class sizes impose restrictions on the group structure. E.g. if the sizes are {1, p}, then the nilpotency class has to be 2. More precisely: the class sizes of a p-group G are {1, p} iff |G′| = p (Knoche; see also Theorem 3 below). But we can ask, e.g., if, given any set S ≠ {1, p} of p-powers, does there exist a group of class 3 ...
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This article describes a setup that – given a composition tree – provides functionality for calculation in finite matrix groups using the Trivial-Fitting approach that has been used successfully for permutation groups. It treats the composition tree as a black-box object. It thus is applicable to other classes of groups for which a composition tree can be obtained. As an example, we consider an...
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We define and study a correspondence between the set of distinguished G0-conjugacy classes in a fixed connected component of a reductive group G (with G0 almost simple) and the set of (twisted) elliptic conjugacy classes in the Weyl group. We also prove a homogeneity property related to this correspondence. Introduction 0.1. Let k be an algebraically closed field of characteristic p ≥ 0 and let...
متن کاملOn Conjugacy Classes of Sl(2, Q)
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: 1971
ISSN: 0021-8693
DOI: 10.1016/0021-8693(71)90086-x