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Units of group rings of groups of order 16

Published online by Cambridge University Press:  18 May 2009

E. Jespers  and
M. M. Parmenter
E. Jespers
Affiliation:
Department of Mathematics and StatisticsMemorial University of Newfoundland St. John's, NewfoundlandCanadaA1C 5S7
M. M. Parmenter
Affiliation:
Department of Mathematics and StatisticsMemorial University of Newfoundland St. John's, NewfoundlandCanadaA1C 5S7
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Let G be a finite group, (ZG) the group of units of the integral group ring ZG and 1(ZG) the subgroup of units of augmentation 1. In this paper, we are primarily concerned with the problem of describing constructively (ZG) for particular groups G. This has been done for a small number of groups (see [11] for an excellent survey), and most recently Jespers and Leal [3] described (ZG) for several 2-groups. While the situation is clear for all groups of order less than 16, not all groups of order 16 were discussed in their paper. Our main aim is to complete the description of (ZG) for all groups of order 16. Since the structure of the unit group of abelian groups is very well known (see for example [10]), we are only interested in the non-abelian case.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 35 , Issue 3 , September 1993 , pp. 367 - 379
Copyright
Copyright © Glasgow Mathematical Journal Trust 1993

References

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