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arXiv · 2003.14193

On Hom-Groups and Hom-Group actions

Liangyun Chen·Tianqi Feng·Yao Ma·Ripan Saha·Hongyi Zhang
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Abstract

A Hom-group is the non-associative generalization of a group, whose associativity and unitality are twisted by a compatible bijective map. In this paper, we give some new examples of Hom-groups, and show the first and the second isomorphism fundamental theorems of homomorphisms on Hom-groups. We also introduce the notion of Hom-group action, and as an application, we show the first Sylow theorem for Hom-groups along the line of group actions.

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Liangyun Chen, Tianqi Feng, Yao Ma, Ripan Saha, Hongyi Zhang. 2020-03-10. On Hom-Groups and Hom-Group actions. https://arxiv.org/abs/2003.14193

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