arXiv · 0705.4681
We compare the random group model of Gromov and the model of generic groups of Arzhantseva and Ol'shanskii.
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Ilya Kapovich, Paul Schupp. 2010-02-08. On group-theoretic models of randomness and genericity. https://arxiv.org/abs/0705.4681
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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.
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