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arXiv · 2606.13430

On a family of non-coset 2-valued groups

Konstantin M. Posadskiy
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Abstract

Within an important class of discrete-time 2-valued dynamical systems on $\mathbb{C}$ defined by polynomials, we extract a family of systems induced by the action of a 2-valued group. We study this 2-valued group and its analogues obtained by replacing $\mathbb{C}$ with an arbitrary field $F$. We establish that all of them are double coset groups. For some of them we prove non-cosetness. In the case $F = \mathbb{C}$, this yields the first example of a topologically non-coset, non-discrete topological 2-valued group.

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Konstantin M. Posadskiy. 2026-06-11. On a family of non-coset 2-valued groups. https://arxiv.org/abs/2606.13430

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