A New Way to Look at Homomorphisms

Guo, Yue

A New Way to Look at Homomorphisms

dc.contributor.advisor	Hawthorn, Ian
dc.contributor.author	Guo, Yue
dc.date.accessioned	2013-09-02T23:18:34Z
dc.date.available	2013-09-02T23:18:34Z
dc.date.issued	2013
dc.date.updated	2013-06-13T23:13:37Z
dc.description.abstract	This thesis is about arbitrary functions between groups. We look at two way to measure how close an arbitrary function is to being a homomorphism. We first look at an action of the group on functions in which homomorphisms are invariant. We also look at distributors, structures which are similar to commutators and which are trivial for a homomorphism. This leads to a rich and interesting theory and gives us a new way to look at homomorphisms and new tools to try to build homomorphisms from arbitrary functions. We demonstrate the applicability of these tools by constructing several alternate proofs of the Schur-Zassenhaus theorem.
dc.format.mimetype	application/pdf
dc.identifier.citation	Guo, Y. (2013). A New Way to Look at Homomorphisms (Thesis, Master of Science (MSc)). University of Waikato, Hamilton, New Zealand. Retrieved from https://hdl.handle.net/10289/7949	en
dc.identifier.uri	https://hdl.handle.net/10289/7949
dc.language.iso	en
dc.publisher	University of Waikato
dc.rights	All items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated.
dc.subject	Distributors
dc.subject	Conjugation of Functions
dc.subject	Cauchy Theorem
dc.subject	Transfer Maps
dc.subject	Schur-Zassenhaus Theorem
dc.title	A New Way to Look at Homomorphisms
dc.type	Thesis
pubs.place-of-publication	Hamilton, New Zealand	en_NZ
thesis.degree.grantor	University of Waikato
thesis.degree.level	Masters
thesis.degree.name	Master of Science (MSc)