Martin Hertweck

On the Torsion Units of Some Integral Group Rings

It is shown that any torsion unit of the integral group ring ZG of a flnite group G is rationally conjugate to a trivial unit if G = P o A with P a normal Sylow p-subgroup of G and A an abelian p 0 -group (thus conflrming a conjecture of Zassenhaus for this particular class of groups). The proof is an application of a fundamental result of Weiss. It is also shown that the Zassenhaus conjecture holds for PSL(2;7), the flnite simple group of order 168. 2000 Mathematics Subject Classiflcation: primary 16S34, 16U60; secondary 20D15

ZASSENHAUS CONJECTURE FOR CENTRAL EXTENSIONS OF S5

Abstract We confirm a conjecture of Zassenhaus about rational conjugacy of torsion units in integral group rings for a covering group of the symmetric group S 5 and for the general linear group GL(2, 5). The first result, together with others from the literature, settles the conjugacy question for units of prime-power order in the integral group ring of a finite Frobenius group.

TORSION UNITS IN INTEGRAL GROUP RINGS OF CERTAIN METABELIAN GROUPS

It is shown that any torsion unit of the integral group ring

Local analysis of the normalizer problem

\mathbb{Z}G

Class-preserving automorphisms and the normalizer property for Blackburn groups

of a finite group

Finite groups of units and their composition factors in the integral group rings of the groups PSL(2,q)

G

The Orders of Torsion Units in Integral Group Rings of Finite Solvable Groups

is rationally conjugate to an element of

ON PRINCIPAL BLOCKS OF p-CONSTRAINED GROUPS

\pm G

Unit Groups of Integral Finite Group Rings with No Noncyclic Abelian Finite p-Subgroups

if

On hypercentral units in integral group rings

G=XA