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arXiv · 2610.04274

Groups of Class Transpositions with Prescribed Prime Divisors of the Moduli

Alex Iskra
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Abstract

For a set $\mathcal P$ of odd primes, let $\operatorname{CT}_{\mathcal P}(\mathbb{Z})$ denote the group generated by all class transpositions whose moduli have no odd prime divisors outside $\mathcal P$. We prove that \[ \bigl\langle \operatorname{CT}_{\mathcal P_1}(\mathbb{Z}),\operatorname{CT}_{\mathcal P_2}(\mathbb{Z}) \bigr\rangle = \operatorname{CT}_{\mathcal P_1\cup\mathcal P_2}(\mathbb{Z}) \] for any sets $\mathcal P_1$ and $\mathcal P_2$ of odd primes. This gives a negative answer to Question 21.75 in the Kourovka Notebook.

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Alex Iskra. 2026-10-03. Groups of Class Transpositions with Prescribed Prime Divisors of the Moduli. https://arxiv.org/abs/2610.04274

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