Footnote to a theorem of Phagan on actions of a cyclic group
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 S of a cyclic group with the number of orbits of the induced action H S of a subgroup H ⊂eq G. This combinatorial fact has applications to notions of arithmetic similarity of number fields, as investigated by Phagan (op. cit.).
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