On the first Zassenhaus conjecture for integral group rings

Victor Bovdi, C. Höfert, W. Kimmerle

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)

Abstract

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).

Original languageEnglish
Pages (from-to)291-303
Number of pages13
JournalPublicationes Mathematicae
Volume65
Issue number3-4
Publication statusPublished - 2004
Externally publishedYes

Keywords

  • Torsion units
  • Zassenhaus conjecture

ASJC Scopus subject areas

  • Mathematics(all)

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