Let G be a finite group and let p be a prime such that (p, |G|) = 1. We study conditions under which the Abelian group Fp[G] has a few G-orbits whose union generate it as an expander (equivalently, all the discrete Fourier coefficients (in absolute value) of this generating set are bounded away uniformly from one). We prove a (nearly sharp) bound on the distribution of dimensions of irreducible...

Let R be a commutative ring with identity. If G is a group, then one can form the group algebra of G over R which we shall denote by R[G]. One can then ask the basic question, how much information about the group G can be deduced from the F-algebra R[G]7 A slightly different formulation is to assume that G and //are groups with R[G] isomorphic to R[H] as /^-algebras and to ask what relations ex...

We consider the permutation group algebra defined by Cameron and show that if the permutation group has no finite orbits, then no homogeneous element of degree one is a zero-divisor of the algebra. We proceed to make a conjecture which would show that the algebra is an integral domain if, in addition, the group is oligomorphic. We go on to show that this conjecture is true in certain special ca...

We generalise group algebras to other algebraic objects with bounded Hilbert space representation theory the generalised group algebras are called “host” algebras. The main property of a host algebra, is that its representation theory should be isomorphic (in the sense of the Gelfand–Raikov theorem) to a specified subset of representations of the algebraic object. Here we obtain both existence ...

In this survey we collect and present the classical and some recent methods to compute the primitive (central) idempotents in semisimple group algebras. MSC 2010. 20C05, 20C15, 16S34, 16U60.

Frobenius algebras play an important role in the representation theory of finite groups. In the present work, we investigate the (quasi) Frobenius property of n-group algebras. Using the (quasi-) Frobenius property of ring, we can obtain some information about constructions of module category over this ring ([2], p. 66–67).

Abstract Let N and H be groups, let G an extension of by . In this article, we describe the structure complex group ring in terms data associated with particular, present conditions on building blocks guaranteeing that satisfies zero-divisor idempotent conjectures. Moreover, for central extensions involving amenable groups Kadison–Kaplansky conjecture holds C $$^*$$ <mml:math xmlns:mml="http://...