Recent work on central units of integral group rings is surveyed. In particular we present two methods of constructing central units, induction and lifting, and demonstrate how these constructions can often be used to find generators for large subgroups in the full group of central units of an integral group ring.

certain algebraic invariants of the integral group ring zg of a group g were introduced and investigated in relation to the problem of extending the farrell-tate cohomology, which is defined for the class of groups of finite virtual cohomological dimension. it turns out that the finiteness of these invariants of a group g implies the existence of a generalized farrell-tate cohomology for g whic...

We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the Mathieu sporadic group M 12. As a consequence, we confirm for this group the Kimmerle's conjecture on prime graphs.

Using the Luthar–Passi method, we investigate the Zassenhaus and Kimmerle conjectures for normalized unit groups of integral group rings of the Held and O’Nan sporadic simple groups. We confirm the Kimmerle conjecture for the Held simple group and also derive for both groups some extra information relevant to the classical Zassenhaus conjecture. Let U(ZG) be the unit group of the integral group...

Abstract The classifying map of the integral Krichever–Hoehn formal group law is presented as a quotient Lazard ring by some explicit ideal.

We investigate the possible character values of torsion units of the normalized unit group of the integral group ring of Mathieu sporadic groupM22. We confirm the Kimmerle conjecture on prime graphs for this group andspecify the partial augmentations for possible counterexamples to the stronger Zassenhaus conjecture.

A free bimodule resolution is constructed for the integral group ring of the dihedral group of order 4m. This resolution is applied for a description, in terms of generators and defining relations, of the Hochschild cohomology algebra of this group ring. Introduction Let K be a commutative ring with unity, let R be an associative K-algebra that is a finitely generated projective K-module, let Λ...

In this article we construct free groups and subgroups of finite index in the unit group of the integral group ring of a finite non-abelian group G for which every non-linear irreducible complex representation is of degree 2 and with commutator subgroup G′ a central elementary abelian 2-group.

We investigate the possible character values of torsion units of thenormalized unit group of the integral group ring of Mathieu sporadic groupM22. We confirm the Kimmerle conjecture on prime graphs for this group andspecify the partial augmentations for possible counterexamples to the strongerZassenhaus conjecture.

Let V (ZG) be the normalized unit group of the integral group ring ZG of a finite group G. One of most interesting conjectures in the theory of integral group ring is the conjecture (ZC) of H. Zassenhaus [25], saying that every torsion unit u ∈ V (ZG) is conjugate to an element in G within the rational group algebra QG. For finite simple groups, the main tool of the investigation of the Zassenh...