On the Number of Characters in Blocks of Finite General Linear, Unitary and Symmetric Groups.
A modular analogue of the well-known group theoretical result about finiteness of the derived subgroup in a group with a finite factor by its center has been obtained.
This work presents an approach towards the representation theory of the braid groups . We focus on finite-dimensional representations over the field of Laurent series which can be obtained from representations of infinitesimal braids, with the help of Drinfeld associators. We set a dictionary between representation-theoretic properties of these two structures, and tools to describe the representations thus obtained. We give an explanation for the frequent apparition of unitary structures on classical...
Let be a finite nonabelian group, its associated integral group ring, and its augmentation ideal. For the semidihedral group and another nonabelian 2-group the problem of their augmentation ideals and quotient groups is deal with. An explicit basis for the augmentation ideal is obtained, so that the structure of its quotient groups can be determined.
We give the characterization of the unit group of , where is a finite field with elements for prime and denotes the special linear group of matrices having determinant over the cyclic group .