On the first Zassenhaus conjecture for integral group rings

Details On the first Zassenhaus conjecture for integral group rings On the first Zassenhaus conjecture for integral group rings

2005-07-12

arxiv.org/abs/math/0507246v1

Publ. Math. Debrecen 65 (2004), no. 3-4, 291--303

Mathematics

Group Theory

Scientific paper

It was conjectured by H. Zassenhaus that a torsion unit of an integral group ring of a finite group is conjugate to a group element within the rational group algebra. The object of this note is the computational aspect of a method developed by I.S. Luthar and I.B.S. Passi which sometimes permits an answer to this conjecture. We illustrate the method on certain explicit examples. We prove with additional arguments that the conjecture is valid for any 3-dimensional crystallographic point group. Finally we apply the method to generic character tables and establish a p-variation of the conjecture for the simple groups PSL(2,p).

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