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arXiv · 2311.11497

Transitive and non-transitive subgroups of permutation groups

Arda Demirhan·Jacob Miller·Yixu Qiu·Thomas J. Tucker·Zheng Zhu
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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.

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Arda Demirhan, Jacob Miller, Yixu Qiu, Thomas J. Tucker, Zheng Zhu. 2023-11-20. Transitive and non-transitive subgroups of permutation groups. https://arxiv.org/abs/2311.11497

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