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, second and third isomorphism theorems of Hom-groups. We also introduce the notion of Hom-group action, and as an application, we prove the first Sylow theorem for Hom-groups along the line of group actions.
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Acknowledgements We give our warmest thanks to the referees for their time and comments.
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Supported by NSF of Jilin Province (Grant No. YDZJ202201ZYTS589), NNSF of China (Grant Nos. 12271085, 12071405) and the Fundamental Research Funds for the Central Universities
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Chen, L.Y., Feng, T.Q., Ma, Y. et al. On Hom-groups and Hom-group Actions. Acta. Math. Sin.-English Ser. 39, 1887–1906 (2023). https://doi.org/10.1007/s10114-023-2133-7
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DOI: https://doi.org/10.1007/s10114-023-2133-7