Sums of binomial coefficients modulo $p$ and groups of exponent $p^n$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912009682944000 |
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| author | Szechtman, Fernando |
| author_facet | Szechtman, Fernando |
| contents | We give a simple matrix-based proof of congruence equations modulo a prime $p$ involving sums of binomial coefficients appearing in Pascal's triangle. These equations can be used to construct some groups of exponent $p^n$. These groups, as well as others of exponent $p^{n+1}$, explain why $p=2$ is not really an exceptional prime in relation to the Heisenberg group over the field with $p$ elements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10352 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sums of binomial coefficients modulo $p$ and groups of exponent $p^n$ Szechtman, Fernando Number Theory Group Theory We give a simple matrix-based proof of congruence equations modulo a prime $p$ involving sums of binomial coefficients appearing in Pascal's triangle. These equations can be used to construct some groups of exponent $p^n$. These groups, as well as others of exponent $p^{n+1}$, explain why $p=2$ is not really an exceptional prime in relation to the Heisenberg group over the field with $p$ elements. |
| title | Sums of binomial coefficients modulo $p$ and groups of exponent $p^n$ |
| topic | Number Theory Group Theory |
| url | https://arxiv.org/abs/2405.10352 |