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PreprintarXiv licencearXiv

Subindices and subfactors of ℤn and k-index stability of finite groups

  • M. H. Hooshmand
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Abstract

We study subindices, subfactors, and index stability in the cyclic group ℤn. We prove several theorems that not only confirm a conjecture and resolve some open problems about index stability of such groups, but also provide basic tools for the characterization of finite k-index stable groups. As a consequence, we completely characterize all 2-element index stable subsets of ℤn, obtain an exact closed formula for their density, and determine all n for which every 2-subset is index unstable. Finally, we present some problems and a research project extending the study to 3-subsets and general k-subsets.

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Cite

BibTeXRIS
BibTeX
@misc{hooshmand2026subindices,
  title = {{Subindices and subfactors of $\mathbbZ_n$ and $k$-index stability of finite groups}},
  author = {M. H. Hooshmand},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.08805},
  eprint = {2607.08805},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.08805},
}
RIS
TY  - UNPB
TI  - Subindices and subfactors of ℤ_n and k-index stability of finite groups
AU  - M. H. Hooshmand
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2607.08805
UR  - https://arxiv.org/abs/2607.08805
AB  - We study subindices, subfactors, and index stability in the cyclic group ℤ_n. We prove several theorems that not only confirm a conjecture and resolve some open problems about index stability of such groups, but also provide basic tools for the characterization of finite k-index stable groups. As a consequence, we completely characterize all 2-element index stable subsets of ℤ_n, obtain an exact closed formula for their density, and determine all n for which every 2-subset is index unstable. Finally, we present some problems and a research project extending the study to 3-subsets and general k-subsets.
ER  -