The Locally Free Cancellation Property of The Group Ring Zg (Eichler Condition, Quaternion Group, Kernel Group)

It is of the utmost importance to know whether ZG has locally free cancellation in many applications where ZG is the integral group ring of a finite group G over Z. Jacobinski's cancellation theorem implies that cancellation holds unless some quotient G/N is a binary poly- hedral group. Swan's theorem which investigates the extent to which the converse of Jacobinski's cancellation theorem holds says that cancellation fails for ZG if G has a quotient which is a binary poly- hedral group but not one of the following seven groups Q(,8), Q(,12), Q(,16), Q(,20), (')T, (')O, and (')I. However, this does not yet characterize the groups for which cancellation fails.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Chen, Hsin-Fong

• Mathematics

Identifier

(UMI)AAI8701454

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/71242