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

School of Computing, Jordanstown Campus, Ulster University, Northern Ireland BT37 0QB, UK
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 (Springer, 2017).
Symmetry 2019, 11(7), 877; https://doi.org/10.3390/sym11070877
Received: 18 June 2019 / Revised: 1 July 2019 / Accepted: 2 July 2019 / Published: 3 July 2019
(This article belongs to the Special Issue Interactions between Group Theory, Symmetry and Cryptology)
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Abstract

It is known that every element in the alternating group A n , 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. View Full-Text
Keywords: group theory; symmetry; Engel words; alternating group group theory; symmetry; Engel words; alternating group
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Martínez Carracedo, J. A Computational Approach to Verbal Width for Engel Words in Alternating Groups. Symmetry 2019, 11, 877.

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