On fundamental properties of hom-groups

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.

کلیدواژه ها:

Hom-group ، Hom-normal subgroup ، Hom-quotient group ، Hom-group homomorphism