Power-conjugate equations in symmetric groups
Combinatorics
2023-10-03 v7 Group Theory
Abstract
We investigate the solutions of the conjugate equation aya^(-1)=y^e in the symmetric group S_{n}. Here a is a fixed (constant), e is an integer exponent and y is a single unknown permutation (in S_{n}). It turns out that the existence of a non-trivial solution y heavily depends on e and the type of a.
Cite
@article{arxiv.2104.03593,
title = {Power-conjugate equations in symmetric groups},
author = {Szilvia Homolya and Jenő Szigeti},
journal= {arXiv preprint arXiv:2104.03593},
year = {2023}
}