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.
|Title of host publication||Computational Mathematics, Numerical Analysis and Applications|
|Subtitle of host publication||Lecture Notes of the XVII 'Jacques-Louis Lions' Spanish-French School|
|Publication status||Published - 2017|
Martinez Carracedo, J., & Martinez Lopez, C. (2017). A Computational Approach to Verbal Width in Alternating Groups. In Computational Mathematics, Numerical Analysis and Applications: Lecture Notes of the XVII 'Jacques-Louis Lions' Spanish-French School (1 ed., Vol. 13). Springer Cham.