Sums of binomial coefficients modulo $p$ and groups of exponent $p^n$

Fernando Szechtman

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arXiv · 2405.10352

Sums of binomial coefficients modulo $p$ and groups of exponent $p^n$

Fernando Szechtman

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Abstract

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.

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Fernando Szechtman. 2024-05-16. Sums of binomial coefficients modulo $p$ and groups of exponent $p^n$. https://arxiv.org/abs/2405.10352

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