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arXiv · 2407.13636

A sieve formula for chains of $p$-subgroups

Elias Schwesig
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Abstract

Given a finite group $G$ and a prime $p$, we establish the sieve formula, which is a congruence containing as summands numbers of chains of $p$-subgroups of $G$ of certain orders. This generalises the Theorem of Sylow-Frobenius, using Wielandt's approach. Its name stems from the sieve formula from set theory because of formal similarities.

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Elias Schwesig. 2024-07-18. A sieve formula for chains of $p$-subgroups. https://arxiv.org/abs/2407.13636

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