Conjugacy classes and straight elements in Coxeter groups
نویسندگان
چکیده
منابع مشابه
Conjugacy of Coxeter Elements
For a Coxeter group (W,S), a permutation of the set S is called a Coxeter word and the group element represented by the product is called a Coxeter element. Moving the first letter to the end of the word is called a rotation and two Coxeter elements are rotation equivalent if their words can be transformed into each other through a sequence of rotations and legal commutations. We prove that Cox...
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Let (W, S, Γ) be an irreducible finitely presented Coxeter system. The present paper is mainly concerned with conjugacy relation on Coxeter elements in the case where Γ containing just one circle, in particular when Γ is itself a circle. In the cases where Γ is either a three multiple circle or a circle with three nodes, we show that the ss-equivalence relation on Coxeter elements of W is the s...
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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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Suppose $G$ is a finite group, $A$ and $B$ are conjugacy classes of $G$ and $eta(AB)$ denotes the number of conjugacy classes contained in $AB$. The set of all $eta(AB)$ such that $A, B$ run over conjugacy classes of $G$ is denoted by $eta(G)$.The aim of this paper is to compute $eta(G)$, $G in { D_{2n}, T_{4n}, U_{6n}, V_{8n}, SD_{8n}}$ or $G$ is a decomposable group of order $2pq$, a group of...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2014
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2014.03.008