A Computational Approach to Verbal Width in Alternating Groups

Jorge Martinez Carracedo; Consuelo Martinez Lopez

A Computational Approach to Verbal Width in Alternating Groups

Jorge Martinez Carracedo, Consuelo Martinez Lopez

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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.

Original language	English
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
Publisher	Springer Cham
Volume	13
Edition	1
ISBN (Electronic)	978-3-319-49631-3
ISBN (Print)	978-3-319-49630-6
Publication status	Published (in print/issue) - 2017

Cite this

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AB - 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.

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A Computational Approach to Verbal Width in Alternating Groups

Abstract

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