E-Groups and isomorphism theorems

Document Type : Research Paper

Author

Department of Mathematics, Payame Noor University, Tehran, Iran

Abstract

We present and explore the fundamental structural theory of e-groups, a generalization of groups introduced by Borumand et al. (2018). We introduce the notions of full e-subgroups and normal full e-subgroups, and we construct the quotient of an e-group under these conditions. Moreover, we define and investigate generated e-subgroups, establish their basic properties, and characterize cyclic e-subgroups. A detailed analysis of the kernel of an e-homomorphism reveals that the subset kernel is not suitable for isomorphism theorems; to resolve this, we adopt the universal algebraic perspective and employ the congruence kernel. Using this approach, we establish the First Isomorphism Theorem for e-groups and provide concrete examples illustrating the result. Furthermore, we discuss the formulation of the Second and Third Isomorphism Theorems within the congruence framework, and we examine the relationship between congruences and normal full e-subgroups.

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References

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History

  • Receive Date: 18 February 2026
  • Revise Date: 10 May 2026
  • Accept Date: 22 May 2026

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