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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.16498 |
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| _version_ | 1866912073581068288 |
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| author | Brusyanskaya, Elena K. |
| author_facet | Brusyanskaya, Elena K. |
| contents | Our result contains as special cases the Frobenius theorem (1895) on the~number of solutions to the equation $x^n=1$ in a finite group and the Solomon theorem (1969) on the number of solutions in a group to systems of equations with fewer equations than unknowns. Instead of systems of equations, we consider arbitrary first-order formulae in the group language with constants. Our result substantially generalizes the Klyachko--Mkrtchyan theorem (2014) on this topic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_16498 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the number of tuples of group elements satisfying a first-order formula Brusyanskaya, Elena K. Group Theory Our result contains as special cases the Frobenius theorem (1895) on the~number of solutions to the equation $x^n=1$ in a finite group and the Solomon theorem (1969) on the number of solutions in a group to systems of equations with fewer equations than unknowns. Instead of systems of equations, we consider arbitrary first-order formulae in the group language with constants. Our result substantially generalizes the Klyachko--Mkrtchyan theorem (2014) on this topic. |
| title | On the number of tuples of group elements satisfying a first-order formula |
| topic | Group Theory |
| url | https://arxiv.org/abs/2306.16498 |