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Units in Integral Group Rings of Some Metacyclic Groups

Published online by Cambridge University Press:  20 November 2018

P. J. Allen  and
C. Hobby
P. J. Allen
Affiliation:
Department of Mathematics University of Aeabama University, AL 35486
C. Hobby
Affiliation:
Department of Mathematics University of Aeabama University, AL 35486
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Abstract

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Let p be odd prime and suppose that G = 〈a, b〉 where ap-1 = bp = 1, a-1 ba = br, and r is a generator of the multiplicative group of integers mod p. An explicit characterization of the group of normalized units V of the group ring ZG is given in terms of a subgroup of GL(p - 1, Z). This characterization is used to exhibit a normal complement for G in V.

Keywords

Primary 20D15Secondary 16A2620C05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 2 , 01 June 1987 , pp. 231 - 240
Copyright
Copyright © Canadian Mathematical Society 1987

References

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