Abstract
We show that the ring of polynomial invariants C[X 1,X 2,X 3] A 3 of the alternating group A 3 is the smallest ring of polynomial invariants of a permutation group, which has no finite SAGBI basis w.r.t. any admissible order. “Smallest” refers to the number of variables, which is 3, and to the number of generators of the invariant ring, which is 4.
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