Hawthorn, IanGuo, Yue2013-09-022013-09-022013Guo, 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/10289/7949https://hdl.handle.net/10289/7949This 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.application/pdfenAll items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated.DistributorsConjugation of FunctionsCauchy TheoremTransfer MapsSchur-Zassenhaus TheoremThesis2013-06-13