Year: 2026
Type: preprint
Abstract: We study subindices, subfactors, and index stability in the cyclic group $\mathbb{Z}_n$. 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 $\mathbb{Z}_n$, 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.
Source: arXiv (Cornell University)
Author: Hooshmand, M. H.
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7168137779