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Metadata 
bibkey: bergerfelzenbaumfraenkel1986herzogschonheim
authors: Marc A. Berger; Alexander Felzenbaum; Aviezri Fraenkel
year: 1986
title: The Herzog-Schonheim Conjecture for Finite Nilpotent Groups
doi: 10.4153/CMB-1986-050-0
claim: Every partition of a finite nilpotent group into r >= 2 left cosets contains two cosets whose subgroups have the same index.
strata_touched:
  - D5/S3/Factorization/PrimePowers/FiniteCosetPartitionMaximalIndexMultiplicity
license: citation-only
triage: anchor

The Herzog-Schonheim Conjecture for Finite Nilpotent Groups

Berger, Felzenbaum, and Fraenkel prove the qualitative repeated-index theorem for finite nilpotent groups: every partition into at least two left cosets (r >= 2) contains two cosets whose underlying subgroups have the same index. This note attests only that qualitative conclusion. It does not attest the stronger p-divisibility or maximal-index multiplicity bound formalized by the referenced D5 module.

Verified locator

  • DOI: https://doi.org/10.4153/CMB-1986-050-0