English

The Herzog-Sch\"onheim conjecture for solvable groups

Combinatorics 2019-03-04 v2 Group Theory

Abstract

Herzog and Sch\"onheim conjectured that any nontrivial partition of a group into cosets must contain two cosets with the same index.

Keywords

Cite

@article{arxiv.1901.10131,
  title  = {The Herzog-Sch\"onheim conjecture for solvable groups},
  author = {Michael C. Burkhart},
  journal= {arXiv preprint arXiv:1901.10131},
  year   = {2019}
}

Comments

The case that a subgroup maps to a full copy of $\ZZ_p$ under the quotient is not trivial and must be considered more carefully

R2 v1 2026-06-23T07:25:08.494Z