Journal of Scientific Research and Reports

Identification, Generating and Classification of Morphisms between Finite Groups

D. Samaila *

Department of Mathematics, Faculty of Science and Science Education, Adamawa State University, P.O.Box 25 Mubi, Nigeria.

M. Pius Pur

Department of Mathematics, Faculty of Science and Science Education, Adamawa State University, P.O.Box 25 Mubi, Nigeria.

*Author to whom correspondence should be addressed.

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Abstract

Our goal in this paper is to generate functions fi from a finite group G to itself such that each fi’^s are morphisms. The concept of the fundamental theorem of finite Abelian group was introduced and we proved the result that if G is any finite Abelian group, then the factor group G/H with H a subgroup of G, is a finite Abelian group. Also, if G = Z_r ⊗ Z_s ⊗ Z_t, then G ≅ Z_r ⊗ Z_s ⊗ Z_t where r,s,t∈Z⁺. We finally conclude on identifying some homomorphisms and automorphisms on finite groups by listing all the possible maps from the group to itself with the help of GAP.

Keywords: Finite group, homomorphism, isomorphism, automorphism, factor group

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