2015/06/24 by Ian Hawthorn, Yue Guo, Hawthorn, Ian +1
Mathematics · #20D99 #FOS: Mathematics #Group Theory (math.GR) #Mathematics and Applications #math.GR #msc:20D99
paper · pdf · doi:10.48550/arxiv.1506.07235
9 pages
arxiv created 2015/06/24 · openalex publication_date 2015/06/24 · arxiv updated 2015/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.