A Computational Approach to Verbal Width for Engel Words in Alternating Groups

Jorge Martinez Carracedo

doi:10.3390/sym11070877

A Computational Approach to Verbal Width for Engel Words in Alternating Groups

Jorge Martinez Carracedo

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Abstract

It is known that every element in the alternating group An, with n≥5, can be written as a product of at most two Engel words of arbitrary length. However, it is still unknown if every element in an alternating group is an Engel word of Arbitrary length. In this paper, a different approach to this problem is presented, getting new results for small alternating groups.

This paper is an extended version of our paper published in Lecture Notes of the XVII ’Jacques-Louis Lions’ Spanish-French School. Computational Mathematics, Numerical Analysis and Applications

Original language	English
Number of pages	12
Journal	Symmetry
Volume	11
Issue number	7
DOIs	https://doi.org/10.3390/sym11070877
Publication status	Published (in print/issue) - 3 Jul 2019

Keywords

group theory
symmetry
engel words
alternating group

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abstract = "It is known that every element in the alternating group An, with n≥5, can be written as a product of at most two Engel words of arbitrary length. However, it is still unknown if every element in an alternating group is an Engel word of Arbitrary length. In this paper, a different approach to this problem is presented, getting new results for small alternating groups.This paper is an extended version of our paper published in Lecture Notes of the XVII {\textquoteright}Jacques-Louis Lions{\textquoteright} Spanish-French School. Computational Mathematics, Numerical Analysis and Applications ",

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KW - group theory

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KW - engel words

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A Computational Approach to Verbal Width for Engel Words in Alternating Groups

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Keywords

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