On finite linear groups II

Representation theory of finite groups II: Linear algebra

Finite p-groups with few non-linear irreducible character kernels

Abstract. In this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.

Non-linear residually finite groups

We prove that groups 〈a, b, t | tat = a, tbt = b〉 are not linear provided k, l 6∈ {−1, 1}. As a consequence we obtain the first example of a non-linear residually finite 1related group.

Linear Representations of Finite Groups

Almost simple groups with Socle $G_2(q)$ acting on finite linear spaces

 After the classification of the flag-transitive linear spaces, the attention has been turned to line-transitive linear spaces. In this article, we present a partial classification of the finite linear spaces $mathcal S$ on which an almost simple group $G$ with the socle $G_2(q)$ acts line-transitively.