Homomorphisms and decompositions in finite generalized groups

Articles in Press

Document Type : Research Paper

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Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

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.
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References

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[2] J. Ara´ujo and J. Konieczny, Molaei’s generalized-groups are completely simple semigroups, Bul. Inst. Politeh. Ia¸si. Sect¸. I. Mat. Mec. Teor. Fiz., 48 (2002), no. 1-2, 1–5.
[3] M. R. Molaei, Generalized groups, Proceeding of the International Conference on Algebra, (1998), 14–17.
[4] M. R. Molaei, Generalized actions, in Geometry, Integrability and Quantization (Varna), (1999), 175–179.
[5] N. Shajareh Poursalavati, Some properties of finite Generalized-groups, J. Mahani Math. Res., 13 (2024), 101–107.
[6] J. D. H. Smith, An introduction to quasigroups and their representations, CRC Press, 2007.
Mathematics and Society

Articles in Press, Accepted Manuscript
Available Online from 21 June 2026

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History

  • Receive Date: 01 December 2025
  • Revise Date: 08 March 2026
  • Accept Date: 21 June 2026
  • Publish Date: 21 June 2026

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