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.

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