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A Remark on the Group Rings of Order Preserving Permutation Groups

Published online by Cambridge University Press:  20 November 2018

R.H. LaGrange  and
A.H. Rhemtulla
R.H. LaGrange
Affiliation:
University of Alberta
A.H. Rhemtulla
Affiliation:
University of Alberta
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If G and H are two groups such that their integral group rings Z(G) and Z(H) are isomorphic, does it follow that G and H are isomorphic? This is the isomorphism problem and an affirmative answer is obtained in case G is a sub group of the group of order preserving permutations of a totally ordered set.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 5 , December 1968 , pp. 679 - 680
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Conrad, P., Right-ordered groups. Michigan Math. J. 6 (1959) 267-275.Google Scholar
2. Holland, C., The lattice-ordered group of automorphisms of an ordered set. Michigan Math. J. 10 (1963) 399-408.Google Scholar