All even permutations with large support are commutators of generating pairs

Abstract

We establish that any even permutation from A_n moving at least [3n/4] + o(n) points is the commutator of a generating pair of A_n and a generating pair of S_n. From this we deduce an exponential lower bound on the number of systems of transitivity in alternating and symmetric groups.

arXiv comment8 pages, 2 tables