Kavli Affiliate: Zheng Zhu
| First 5 Authors: Arda Demirhan, Jacob Miller, Yixu Qiu, Thomas J. Tucker, Zheng Zhu
| Summary:
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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