Transitive and intransitive subgroups of permutation groups
Copyright policy )Transitive and intransitive subgroups of permutation groups
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.
Mathematics - Number Theory, wreath products, permutation groups, FOS: Mathematics, Subgroup theorems; subgroup growth, General theory for finite permutation groups, Group Theory (math.GR), Number Theory (math.NT), transitive subgroups, Mathematics - Group Theory
Mathematics - Number Theory, wreath products, permutation groups, FOS: Mathematics, Subgroup theorems; subgroup growth, General theory for finite permutation groups, Group Theory (math.GR), Number Theory (math.NT), transitive subgroups, Mathematics - Group Theory
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