Transitive and non-transitive subgroups of permutation groups
Group Theory
2023-11-21 v1 Number Theory
Abstract
We treat the problem of finding transitive subgroups G of S_n containing normal subgroups N_1 and N_2, with N_1 transitive and N_2 not transitive, such that G/N_1 is isomorphic G/N_2. We show that such G exist whenever n has a prime factor that also divides the Euler-phi function of n. We show that no such G exist when n = pq for p < q with p not dividing q-1.
Cite
@article{arxiv.2311.11497,
title = {Transitive and non-transitive subgroups of permutation groups},
author = {Arda Demirhan and Jacob Miller and Yixu Qiu and Thomas J. Tucker and Zheng Zhu},
journal= {arXiv preprint arXiv:2311.11497},
year = {2023}
}