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Group theory
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Erdős problem 274 - herzog schonheim
Let G be a group, and let A={a1G1,…,akGk}
be a finite system of left cosets of
subgroups
G1,…,Gk
of
G
.
Herzog and Schönheim conjectured that if
A
forms a partition of
G
with
k>1
, then the
indices
[G:G1],…,[G:Gk]
cannot be distinct.
Pin rotation in progress; nothing can be submitted right now.
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
Erdős problem 274 - herzog schonheim · Conjectures.io