Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-25T04:21:46.897Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Allen, P.J. and Hobby, C., A Characterization of Units in Z\A4), J. Algebra 66(1980), 534–543.Google Scholar
2. Bhandari, A.K. and Luthar, I.S., Torsion Units of Integral Group Rings of Metacyclic Groups, J. Number Theory 17(1983), 270–283.Google Scholar
3. Cliff, G.H., Sehgal, S.K. and Weiss, A.R., Units of Integral Group Rings ZS3 , Canad. Math. Bull. 15(1972), 529–534.Google Scholar
4. Hall, M., The Theory of Groups, Chelsea, New York, 1976.Google Scholar
5. Hughes, I. and Pearson, K.R., The Group of Units of the Integral Group Ring ZS3 , Canad. Math. Bull. 15(1972), 529–534.Google Scholar
6. Kleinert, E., Einheiten in Z[D2m], J. Number Theory 13(1981), 541–561.Google Scholar
7. Polcino Milies, C., The Units of the Integral Group Ring ZD4 , Bol. Soc. Mat. Brasil 4(1972), 85–92.Google Scholar
8. Ritterand, J. Sehgal, S.K. Integral Group Rings of Some p -Groups, Can. J. Math. 34(1982), 233–246.Google Scholar
9. Sehgal, S.K., Topics in Group Rings, Dekker, New York, 1978.Google Scholar