Arbitrary Functions in Group Theory


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New Zealand Journal of Mathematics

Vol. 45, (2015), Pages 1-9

Ian Hawthorn

Department of Mathematics,

University of Waikato,


New Zealand.

Yue Guo

Abstract 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.

Keywords Arbitrary functions

Classification (MSC2000) 20D99.

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