We calculate the integral cohomology ring structure for various members of the Bianchi group family. The main tools we use are the Bockstein spectral sequence and a long exact sequence derived from Bass-Serre theory.

We study the nullcone for the symplectic group with respect to a joint action of the general linear group and the symplectic group. By extracting an algebra over a distributive lattice structure from the coordinate ring of the nullcone, we describe a toric degeneration and standard monomial theory of the nullcone in terms of double tableaux and integral points in a convex polyhedral cone.

We prove that every amenable group of cohomological dimension two whose integral ring is a domain solvable and investigate certain homological finiteness properties groups satisfy the analytic zero divisor conjecture act on an acyclic CW-complex with stabilisers.

A correction factor naturally arises in the theory of p-adic Kac--Moody groups. In this paper, we expand into a sum irreducible characters underlying algebra. We derive formula for coefficients, which lie ring power series with integral coefficients. case that Weyl group is universal Coxeter group, show coefficients are actually polynomials.

Let Γ be a cocompact Fuchsian group. We calculate the lower algebraic K-theory of the integral group ring ZΓ and find an explicit formula for Ki(ZΓ), i ≤ 1, in terms of the lower K-groups of finite cyclic groups.

We prove the algebraic eigenvalue conjecture of J.Dodziuk, P.Linnell, V.Mathai, T.Schick and S.Yates (see [2]) for sofic groups. Moreover, we give restrictions on the spectral measure of elements in the integral group ring. Finally, we prove a quantization of the operator norm below 2. To the knowledge of the author, there is no group known, which is not sofic.

It is shown that in the units of augmentation one of an integral group ring ZG of a finite group G, a noncyclic subgroup of order p, for some odd prime p, exists only if such a subgroup exists in G. The corresponding statement for p = 2 holds by the Brauer–Suzuki theorem, as recently observed by W. Kimmerle.