Proving the 5-Engel identity in the 2-generator group of exponent four
arxiv(2024)
摘要
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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