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 of S2n + 1 if and only if the following three conditions are satisfied (i) n + 1 ≤ p, q, (ii) 2n + 1 ≥ p, q, (iii) p + q ≥ 3n + 1.
@article{430,
title = {Commutators of cycles in permutation groups},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {9},
year = {2014},
doi = {10.26493/1855-3974.430.eaf},
language = {EN},
url = {http://dml.mathdoc.fr/item/430}
}
Vavpetič, Aleš. Commutators of cycles in permutation groups. ARS MATHEMATICA CONTEMPORANEA, Tome 9 (2014) . doi : 10.26493/1855-3974.430.eaf. http://gdmltest.u-ga.fr/item/430/