Groups whose irreducible representations have degrees dividingp2

On Finite Groups With Two Irreducible Character Degrees

Computing Irreducible Representations of Groups

How can you find a complete set of inequivalent irreducible (ordinary) representations of a finite group? The theory is classical but, except when the group was very small or had a rather special structure, the actual computations were prohibitive before the advent of high-speed computers ; and there remain practical difficulties even for groups of relatively small orders ( á 100). The present ...

Irreducible Representations of Diperiodic Groups

The irreducible representations of all of the 80 diperiodic groups, being the symmetries of the systems translationally periodical in two directions, are calculated. To this end, each of these groups is factorized as the product of a generalized translational group and an axial point group. The results are presented in the form of the tables, containing the matrices of the irreducible represent...

Computing Irreducible Representations of Finite Groups

We consider the bit-complexity of the problem stated in the title. Exact computations in algebraic number fields are performed symbolically. We present a polynomial-time algorithm to find a complete set of nonequivalent irreducible representations over the field of complex numbers of a finite group given by its multiplication table. In particular, it follows that some representative of each equ...

Abelian topological groups without irreducible Banach representations

We exhibit abelian topological groups admitting no nontrivial strongly continuous irreducible representations in Banach spaces. Among them are some abelian Banach–Lie groups and some monothetic subgroups of the unitary group of a separable Hilbert space.