Related papers: z-Classes in Finite Coxeter Groups

In this paper, we give a characterization of Coxeter group representations of Lusztig's a-function value 1, then determine all the irreducible such representations for certain simply laced Coxeter groups.

We classify a class of complex representations of an arbitrary Coxeter group via characters of the integral homology of certain graphs. Such representations can be viewed as a generalization of the geometric representation and correspond to…

The structure of groups for which certain sets of commutator subgroups are finite is investigated, with a particular focus on the relationship between these groups and those with finite derived subgroup.

In his paper "Finite groups have many conjugacy classes" (J. London Math. Soc (2) 46 (1992), 239-249), L. Pyber proved the to date best general lower bounds for the number of conjugacy classes of a finite group in terms of the order of the…

In this note we discuss Morita equivalence classes of arbitrary finitely presented algebras

This abstract presents (without proofs) some new results on commutativity degree of finite groups.

This work gives a classification of imprimitive irreducible finite subgroups of the orthogonal group O(7) plus the number of conjugate classes for each group.

The parameter coclass has been used successfully in the study of nilpotent algebraic objects of different kinds. In this paper a definition of coclass for nilpotent semigroups is introduced and semigroups of coclass 0, 1, and 2 are…

In this note, we study the finite groups with the number of cylic subgroups no greater than 6.

In the paper new criteria of existence and conjugacy of Hall subgroups of finite groups are given.

Folding subgroups give a way to realize non-simply-laced Coxeter groups as subgroups of simply-laced Coxeter groups. In this paper, we study how folding subgroups of finite and affine type are distributed length-wise by calculating the…

In this article we give an elementary introduction to the representation theory of finite magnetic groups from a purely mathematical point of view. -- En este art\'iculo damos una introducci\'on elemental a la teor\'ia de representaciones…

We give formulas for the second and third integral homology of an arbitrary finitely generated Coxeter group, solely in terms of the corresponding Coxeter diagram. The first of these calculations refines a theorem of Howlett, while the…

The paper presents some new results on Z-related sets obtained by computational methods. We give a complete enumeration of all Z-related sets in $\mathbb{Z}_{N}$ for small $N$. Furthermore, we establish that there is a reasonable…

Let W be a Coxeter group with Coxeter generators S. The rank of the Coxeter system (W,S) is the cardinality |S| of S. The Coxeter system (W,S) has finite rank if and only if W is finitely generated. If (W,S) has infinite rank, then |S| =…

The purpose of this article is to shed new light on the combinatorial structure of Kazhdan-Lusztig cells in infinite Coxeter groups $W$. Our main focus is the set $\D$ of distinguished involutions in $W$, which was introduced by Lusztig in…

The authors classify the finite index subgroups of R. Thompson's group $F$. All such groups that are not isomorphic to $F$ are non-split extensions of finite cyclic groups by $F$. The classification describes precisely which finite index…

Finite field transforms have many applications and, in many cases, can be implemented with a low computational complexity. In this paper, the Z Transform over a finite field is introduced and some of its properties are presented.

This document gives a list of finite semigroups that are interesting from the point of view of Krohn-Rhodes complexity theory. The list will be expanded and updates as "time goes by".

We present new classes of permutation polynomials over finite fields.