Finite groups with eight non-linear irreducible characters
This Note contains the complete list of finite groups, having exactly eight non-linear irreducible characters. In section 4 we consider in full details some typical cases.
On the number of solutions of equation in a finite group
Theorem A yields the condition under which the number of solutions of equation in a finite -group is divisible by (here is a fixed positive integer). Theorem B which is due to Avinoam Mann generalizes the counting part of the Sylow Theorem. We show in Theorems C and D that congruences for the number of cyclic subgroups of order which are true for abelian groups hold for more general finite groups (for example for groups with abelian Sylow -subgroups).
Page 1