Hawthorn, I., & Guo, Y. (2015). Arbitrary functions in group theory. New Zealand Journal of Mathematics, 45, 1–9.
Permanent Research Commons link: https://hdl.handle.net/10289/9475
Two measures of how near an arbitrary function between groups is to being a homomorphism are considered. These have properties similar to conjugates and commutators. The authors show that there is a rich theory based on these structures, and that this theory can be used to unify disparate approaches such as group cohomology and the transfer and to prove theorems. The proof of the Schur-Zassenhaus theorem is recast in this context. We also present yet another proof of Cauchy’s theorem and a very quick approach to Sylow’s theorem.
This article has been published in the journal: New Zealand journal of mathematics. Used with permission.