Torsion Units in the Integral Group Ring of the Alternating Group of Degree 6

Abstract

It was conjectured by H. Zassenhaus that a torsion unit of an integral group ring ℤG of a finite group G conjugates to a group element within the rational group algebra ℚG. We investigate the Zassenhaus Conjecture (ZC) and a conjecture by W. Kimmerle about prime graph in the normalized unit group of ℤA₆.

Key Words:

• Alternating groups
• Group of units
• Integral group rings
• Kimmerle's conjecture
• Zassenhaus conjecture

2000 Mathematics Subject Classification:

• Primary 20C05, 20C10
• Secondary 20C06, 16U60

ACKNOWLEDGMENT

Thanks to V. Bovdi and A. Konovalov for their great help in doing LAGUNA.

The article was supported by UAEU Research Support Program for UAE Faculties.

Notes

Communicated by I. P. Shestakov.