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Groups of Class Transpositions with Prescribed Prime Divisors of the Moduli
Abstract
For a set π« of odd primes, let CTπ«(β€) denote the group generated by all class transpositions whose moduli have no odd prime divisors outside π«. We prove that β¨ CTπ«1(β€),CTπ«2(β€) β© = CTπ«1βͺπ«2(β€) for any sets π«1 and π«2 of odd primes. This gives a negative answer to Question 21.75 in the Kourovka Notebook.
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BibTeX
@misc{iskra2026groups,
title = {{Groups of Class Transpositions with Prescribed Prime Divisors of the Moduli}},
author = {Alex Iskra},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04274},
eprint = {2610.04274},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04274},
}
RIS
TY - UNPB
TI - Groups of Class Transpositions with Prescribed Prime Divisors of the Moduli
AU - Alex Iskra
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04274
UR - https://arxiv.org/abs/2610.04274
AB - For a set π« of odd primes, let CT_π«(β€) denote the group generated by all class transpositions whose moduli have no odd prime divisors outside π«. We prove that β¨ CT_π«_1(β€),CT_π«_2(β€) β© = CT_π«_1βͺπ«_2(β€) for any sets π«_1 and π«_2 of odd primes. This gives a negative answer to Question 21.75 in the Kourovka Notebook.
ER -