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A sieve formula for chains of $p$-subgroups

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arxiv 2407.13636 v1 pith:YHEX3FWO submitted 2024-07-18 math.GR

Elias Schwesig This is my paper · ORCID
classification math.GR
keywords formulasievechainssubgroupsapproachbecausecertaincongruence
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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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