Transitive and non-transitive subgroups of permutation groups
Abstract
We treat the problem of finding transitive subgroups G of Sn containing normal subgroups N1 and N2, with N1 transitive and N2 not transitive, such that G/N1 is isomorphic G/N2. 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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