Date of Award

1-1-2020

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (iv, 49 pages) : illustrations.

Dissertation/Thesis Chair

Anupam Srivastav

Committee Members

Marco Varisco, Antun Milas, Boris Goldfarb, Anupam Srivastav

Keywords

Abelian groups, Finite groups, Swan subgroups, Truncated Group Rings, Units, Unit groups (Ring theory), Group rings, Rings of integers

Subject Categories

Physical Sciences and Mathematics

Abstract

In this thesis an analogue of the triviality of units of group rings of finite abelian groupsis proved for truncated group rings. A Higman group is a group of exponent 2, 3, 4 or 6. The truncated group ring ZG t is the quotient of the group ring by the ideal generated by the formal sum of all group elements. We show that in the case of finite abelian G that ZG t has only trivial units; i.e, that any unit in ZG t is an image under the quotient map of a unit of the form ±g, where g ∈ G, if (and only if) G is a Higman group. We additionally show several results that follow from this pertaining to Swan subgroups.

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