Proving the 5-Engel identity in the 2-generator group of exponent four
Combinatorics
2024-01-26 v1 Group Theory
Abstract
It is known that the fifth Engel word is trivial in the 2-generator group of exponent four , and so can be written as a product of fourth powers. Explicit products of 250 and 28 powers are known, using fourth powers of words up to lengths four and ten respectively. Using a reduction technique based on the recursive enumerability of the set of trivial words in a finite presentation we were able to rewrite as a product of 26 fourth powers of words up to length five.
Cite
@article{arxiv.2401.13859,
title = {Proving the 5-Engel identity in the 2-generator group of exponent four},
author = {Colin Ramsay},
journal= {arXiv preprint arXiv:2401.13859},
year = {2024}
}