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Determining Units in Some Integral Group Rings

Published online by Cambridge University Press:  20 November 2018

E. G. Goodaire,
E. Jespers and
M. M. Parmenter
E. G. Goodaire
Affiliation:
Memorial University of Newfoundland, St. John's, Canada, A1C 5S7
E. Jespers
Affiliation:
Memorial University of Newfoundland, St. John's, Canada, A1C 5S7
M. M. Parmenter
Affiliation:
Memorial University of Newfoundland, St. John's, Canada, A1C 5S7
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In this brief note, we will show how in principle to find all units in the integral group ring ZG, whenever G is a finite group such that and Z(G) each have exponent 2, 3, 4 or 6. Special cases include the dihedral group of order 8, whose units were previously computed by Polcino Milies [5], and the group discussed by Ritter and Sehgal [6]. Other examples of noncommutative integral group rings whose units have been computed include , but in general very little progress has been made in this direction. For basic information on units in group rings, the reader is referred to Sehgal [7].

Keywords

16A26

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 2 , 01 June 1990, pp. 242 - 246
Copyright
Copyright © Canadian Mathematical Society 1990

References

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