Computational aspects of subindices and subfactors with characterization of finite index stable groups

Document Type : Research Paper

Authors

1 Department of Mathematics, Shi.C., Islamic Azad University, Shiraz, Iran

2 Department of Mathematical Sciences, Sharif University of Technology, Azadi Avenue, Tehran, 11155-9415, Tehran, Iran

Abstract

Recently, subindices and subfactors of groups with connections to number theory, additive combinatorics, and factorization of groups have been introduced and studied. Since all group subsets are considered in the theory and there are many basic open problems and questions, their computational aspects are of particular importance. In this paper, by introducing some computational methods and using theoretical approaches together, we not only solve several problems but also pave the way for studying the topic. As the most important result of the study, we completely characterize finite index stable groups.

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References

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[3] M. H Hooshmand, Factor subset of finite group, 2014. mathoverflow.net/questions/155986/factor-subset-of-finite-group
[4] M. H. Hooshmand, Basic results on an unsolved problem about factorization of finite groups, Comm. Algebra, 49 no. 7 (2021) 2927–2933.
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International Journal of Group Theory
Volume 15, Issue 3 - Serial Number 3
September 2026
Pages 145-160

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History

  • Receive Date: 14 August 2024
  • Revise Date: 04 August 2025
  • Accept Date: 25 August 2025
  • Published Online: 21 September 2025

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