Andreas Bächle

Rational Conjugacy of Torsion Units in Integral Group Rings of Non-Solvable Groups

We introduce a new method to study rational conjugacy of torsion units in integral group rings using integral and modular representation theory. Employing this new method, we verify the first Zassenhaus conjecture for the group PSL(2, 19). We also prove the Zassenhaus conjecture for PSL(2, 23). In a second application we show that there are no normalized units of order 6 in the integral group rings of M 10 and PGL(2, 9). This completes the proof of a theorem of Kimmerle and Konovalov that shows that the prime graph question has an affirmative answer for all groups having an order divisible by at most three different primes.

HeLP -- A GAP-package for torsion units in integral group rings

We briefly summarize the background of the HeLP-method for torsion units in group rings and present some functionality of a GAP-package implementing it.

On the prime graph question for almost simple groups with an alternating socle

Let

On the Prime Graph Question for Integral Group Rings of 4-Primary Groups II

G

Integral group rings of solvable groups with trivial central units

be an almost simple group with socle

On the prime graph question for integral group rings of 4-primary groups I

A_n

The status of the Zassenhaus conjecture for small groups

, the alternating group of degree

Algorithmic Aspects of Units in Group Rings

n

Groups whose elements are not conjugate to their powers

. We prove that there is a unit of order

A classification of exceptional components in group algebras over abelian number fields

pq