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

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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 languageEnglish
Number of pages12
JournalSymmetry
Volume11
Issue number7
DOIs
Publication statusPublished - 3 Jul 2019

Keywords

  • group theory
  • symmetry
  • engel words
  • alternating group

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