Kourovka Problem 18.50: Every permitted count of permuted products
- Mathematics
For every positive n and 1 ≤ k ≤ n!, a group has n distinct elements whose n! ordered products take exactly k distinct values.
Kourovka Problem 18.50: Every permitted count of permuted products
- Mathematics
For every positive n and 1 ≤ k ≤ n!, a group has n distinct elements whose n!
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Read the background
For every positive n and 1 ≤ k ≤ n!, a group has n distinct elements whose n! ordered products take exactly k distinct values.
Why it matters
A central-extension construction settles every intermediate count in Kourovka Problem 18.50.
What counts as progress
A specific group theory result with documented AI mathematical work, a stated prior baseline and a checkable source.
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Kourovka Problem 18.50: Every permitted count of permuted products