INTEGRAL GROUP RINGS WITH TRIVIAL CENTRAL UNITS II

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.

Central Units of Integral Group Rings of Nilpotent Groups

In this paper a finite set of generators is given for a subgroup of finite index in the group of central units of the integral group ring of a finitely generated nilpotent group. In this paper we construct explicitly a finite set of generators for a subgroup of finite index in the centre Z(U(ZG)) of the unit group U(ZG) of the integral group ring ZG of a finitely generated nilpotent group G. Ri...

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.