On Hom-Groups and Hom-Group actions

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 als...

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Bibliographic Details
Published in:arXiv.org 2020-12
Main Authors: Chen, Liangyun, Feng, Tianqi, Yao, Ma, Saha, Ripan, Zhang, Hongyi
Format: Article
Language:English
Subjects:
Homomorphisms
Isomorphism
Properties (attributes)
Quotients
Online Access:Get full text
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Summary: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.
ISSN:2331-8422