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