Sun · Indices of pairwise disjoint group cosets

If a₁G₁,…,aₖGₖ are pairwise disjoint left cosets of finite-index subgroups of a group G, prove that gcd([G:Gᵢ],[G:Gⱼ])≥k for some i<j.

cosetsfinite indexcovering systems

The problem

If a₁G₁,…,aₖGₖ are pairwise disjoint left cosets of finite-index subgroups of a group G, prove that gcd([G:Gᵢ],[G:Gⱼ])≥k for some i<j.

Open since2004exact formulation year

Last checked2026.07.27Catalog verification

Offer 01$200Zhi-Wei Sun

Personal offer

The author’s official survey offers US$200 for a proof of Conjecture 4.2.