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arXiv · 2606.16858

Footnote to a theorem of Phagan on actions of a cyclic group

Anurag Sahay
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Abstract

We provide a simplified proof of a recent theorem of Phagan (arXiv:2509.14083) relating the number of orbits of a given length of an action $G \curvearrowright S$ of a cyclic group with the number of orbits of the induced action $H \curvearrowright S$ of a subgroup $H \subseteq G$. This combinatorial fact has applications to notions of arithmetic similarity of number fields, as investigated by Phagan (op. cit.).

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Anurag Sahay. 2026-06-15. Footnote to a theorem of Phagan on actions of a cyclic group. https://arxiv.org/abs/2606.16858

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