Commutators of cycles in permutation groups
Commutators of cycles in permutation groups
We prove that for n ≥ 5, every element of the alternating group An is a commutator of two cycles of An. Moreover we prove that for n ≥ 2, a (2n + 1)-cycle of the permutation group S2n + 1 is a commutator of a p-cycle and a q-cycle …