English

A sieve formula for chains of $p$-subgroups

Group Theory 2024-07-19 v1

Abstract

Given a finite group GG and a prime pp, we establish the sieve formula, which is a congruence containing as summands numbers of chains of pp-subgroups of GG 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.

Keywords

Cite

@article{arxiv.2407.13636,
  title  = {A sieve formula for chains of $p$-subgroups},
  author = {Elias Schwesig},
  journal= {arXiv preprint arXiv:2407.13636},
  year   = {2024}
}
R2 v1 2026-06-28T17:46:13.527Z