The elements here are permutations, and a default operation is permutation and combination.
With this operation, closures can be verified directly without relying on association rules.
According to the definition of permutation compound, it can be directly calculated that AB: {v1v2v3 v4} → {v2v1v4 v3} is not in the set {a, b, e}.
The permutation satisfies the associative law about composition, and all 4 yuan permutations form group S4.
These three elements belong to S4, and the conclusion is that {a, b, e} does not constitute a subgroup of S4 (non-closed).
The smallest subgroup of S4 containing a, b and e is {AB, a, b, e}, (AB = BA).
As long as verification is close to operation and inversion, verification is a subgroup.