Kourovka Problem 21.8: Class transpositions generate the full symmetric group
- Mathematics
For k ≥ 4, horizontal class transpositions of moduli at most k generate a group isomorphic to the symmetric group on lcm(2,…,k) letters.
Kourovka Problem 21.8: Class transpositions generate the full symmetric group
- Mathematics
For k ≥ 4, horizontal class transpositions of moduli at most k generate a group isomorphic to the symmetric group on lcm(2,…,k) letters.
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Read the background
For k ≥ 4, horizontal class transpositions of moduli at most k generate a group isomorphic to the symmetric group on lcm(2,…,k) letters.
Why it matters
The proof gives a general group description for Problem 21.8.
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 21.8: Class transpositions generate the full symmetric group