Central units of integral group rings of monomial groups

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...

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

Groups generated by two bicyclic units in integral group rings

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.