Infinite groups admitting a faithful irreducible representation

Minimal Faithful Permutation Degrees for Irreducible Coxeter Groups

The minimal faithful degree of a finite group G, denoted by μ(G), is the least non-negative integer n such that G embeds inside Sym(n). In this article we calculate the minimal faithful permutation degree for all of the irreducible Coxeter groups.

On Irreducible, Infinite, Non-affine Coxeter Groups

The following results are proved: (1) The center of any finite index subgroup of an irreducible, infinite, non-affine Coxeter group is trivial; (2) Any finite index subgroup of an irreducible, infinite, non-affine Coxeter group cannot be expressed as a product of two nontrivial subgroups. These two theorems imply a unique decomposition theorem for a class of Coxeter groups. . MSC 2000 Subject C...

Finite Groups with a Faithful Real-valued Irreducible Character Whose Square Has Exactly Two Distinct Irreducible Constituents

We study the groups satisfying the property stated in the title.

Irreducible Representations of Infinite-dimensional Transformation Groups and Lie Algebras

Finite groups admitting a connected cubic integral bi-Cayley graph

A graph   is called integral if all eigenvalues of its adjacency matrix  are integers.  Given a subset $S$ of a finite group $G$, the bi-Cayley graph $BCay(G,S)$ is a graph with vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid sin S, xin G}$.  In this paper, we classify all finite groups admitting a connected cubic integral bi-Cayley graph.