On the Unit Conjecture for Supersoluble Group Rings, I

Details On the Unit Conjecture for Supersoluble Group Rings, I On the Unit Conjecture for Supersoluble Group Rings, I

2010-10-06

arxiv.org/abs/1010.1144v1

Mathematics

Rings and Algebras

17 pages

Scientific paper

We introduce structure theorems for the study of the unit conjecture for supersoluble group rings and apply our results to the (Passman) fours group G. We show that over any field K, the group algebra KG has no non-trivial units of length at most 3, and find that the Promislow set can never be the support of a unit in KG. We conclude our work with an introduction to the theory of "consistent chains" toward a preliminary analysis of units of higher length in KG.

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