Proving the 5-Engel identity in the 2-generator group of exponent four
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914652561080320 |
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| author | Ramsay, Colin |
| author_facet | Ramsay, Colin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13859 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Proving the 5-Engel identity in the 2-generator group of exponent four Ramsay, Colin Combinatorics Group Theory 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. |
| title | Proving the 5-Engel identity in the 2-generator group of exponent four |
| topic | Combinatorics Group Theory |
| url | https://arxiv.org/abs/2401.13859 |