On fundamental properties of hom-groups

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Federal University of Agriculture, Abeokuta, Nigeria

2 Department of Mathematics, Auburn University, Auburn, AL 36849, USA

3 Department of Mathematical Sciences, Federal University of Oye, Oye-Ekiti, Nigeria

4 Department of Mathematics, University of Lagos, Akoka, Yaba, Lagos, Nigeria

Abstract

This paper focuses on the study of Hom-groups. A Hom-group $(G,\ast,\alpha)$  is the non-associative generalization of the classical group $G$ whose associativity and unitality are twisted by a compatible bijective map $\alpha$. We present more properties of Hom-groups, Hom-subgroups, Hom-normal subgroups, Hom-quotient groups and Hom-group homomorphisms with examples. We prove the Zassenhaus Butterfly Lemma of Hom-groups as a major result of this paper.

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References

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Journal of Mahani Mathematical Research

Articles in Press, Accepted Manuscript
Available Online from 02 January 2025

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History

  • Receive Date: 19 September 2024
  • Revise Date: 15 December 2024
  • Accept Date: 30 December 2024

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