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arXiv · 2401.13859

Proving the 5-Engel identity in the 2-generator group of exponent four

Colin Ramsay
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Abstract

It is known that the fifth Engel word $E_5$ is trivial in the 2-generator group of exponent four $B(2,4)$, 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 $E_5$ as a product of 26 fourth powers of words up to length five.

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Colin Ramsay. 2024-01-24. Proving the 5-Engel identity in the 2-generator group of exponent four. https://arxiv.org/abs/2401.13859

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