Units in integral group rings

Some Results on Hypercentral Units in Integral Group Rings

In this note we investigate the hypercentral units in integral group rings ZG, where G is not necessarily torsion. One of the main results obtained is the following (Theorem 3.5): if the set of torsion elements of G is a subgroup T of G and if Z2(U) is not contained in CU (T ), then T is either an Abelian group of exponent 4 or a Q∗ group. This extends our earlier result on torsion group rings.

Groups generated by two bicyclic units in integral group rings

Torsion units in integral group rings of Janko simple groups

Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of integral group rings of Janko simple groups. As a consequence, for the Janko groups J1, J2 and J3 we confirm Kimmerle’s conjecture on prime graphs.

Torsion Units in Integral Group Rings of Conway Simple Groups

Using the Luthar–Passi method, we investigate the possible orders and partial augmentations of torsion units of the normalized unit group of integral group rings of Conway simple groups Co1, Co2 and Co3. Let U(ZG) be the unit group of the integral group ring ZG of a finite group G, and V (ZG) be its normalized unit group

Central Units in Integral Group Rings II 1

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.