Finite linear groups in seven variables

Finite Linear Groups in Seven Variables

If G is a finite group which has a faithful complex representation of degree n it is said to be a linear group in n variables. This is equivalent to saying G is a finite group of complex linear transformations. I t is customary to consider only unimodular linear transformations. For n ^ 4 these groups have been known for a long time. An account may be found in Blichfeldt's book [ l ] . For n = ...

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.

Variables Separated Equations and Finite Simple Groups

[UMSt] www.math.uci.edu/ ̃mfried/paplist-cov/UMStory.html. Algebraic equations in separated variables: (*) f(x)−g(y) = 0. Defines a projective nonsingular algebraic curve Xf,g with two projections to the (Riemann sphere) z-line Pz = C ∪ {∞}: f : Px → Pz and g : Py → Pz. Two problems from the 60s (Davenport’s and Shinzel’s) solved by the monodromy method . I explain that and the associated Genus ...

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