A computational approach to verbal width in alternating groups

Abstract

We know that every element in an Alternating group An, n ≥ 5, can be written as a Engel word of length two (Carracedo, Extracta Math. 30(2), 251–262, 2015 and J. Algebra Appl. 16(2), 1750021, 10 p., 2017). There is a conjecture that every element in an Alternating group An, n ≥ 5, can be written as an Engel word of arbitrary length. We give here a computational approach to this problem, what allows to prove the conjecture for 5 ≤ n ≤ 14.