A sieve formula for chains of p-subgroups : extending Wielandt’s proof of Sylow-Frobenius to a congruence modulo p^(ℓ+1)

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. Its name stems from the sieve formula from set theory because of formal similarities.