University of Isfahan Mathematics and Society 2345-6493 Articles in Press 2026 06 21 Homomorphisms and decompositions in finite generalized groups Homomorphisms and decompositions in finite generalized groups 30528 10.22108/msci.2026.147643.1777 FA Nosratollah Shajareh Poursalavati Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran Journal Article 2025 12 01 This paper presents a comprehensive analysis of the interaction between homomorphisms and decomposition theorems in finite generalized groups. By synthesizing the theory of homomorphisms and external structures with decomposition theorems, we obtain new results about the structure of finite strongly normal generalized groups. We introduce the concept of homomorphic decomposition and prove that every finite strongly normal generalized group can be decomposed into the direct product of its image under a homomorphism and a kernel structure. We also establish conditions under which the decomposition preserves homomorphic properties. Our results provide a unified framework for understanding the structure of finite generalized groups and their homomorphisms. \end{abstract} This paper presents a comprehensive analysis of the interaction between homomorphisms and decomposition theorems in finite generalized groups. By synthesizing the theory of homomorphisms and external structures with decomposition theorems, we obtain new results about the structure of finite strongly normal generalized groups. We introduce the concept of homomorphic decomposition and prove that every finite strongly normal generalized group can be decomposed into the direct product of its image under a homomorphism and a kernel structure. We also establish conditions under which the decomposition preserves homomorphic properties. Our results provide a unified framework for understanding the structure of finite generalized groups and their homomorphisms. \end{abstract} https://math-sci.ui.ac.ir/article_30528_64291c3ee0f40eb4f8f7a1adab4b27fe.pdf