Question

Find the order of the permutation
group on three symbols. Also write
down the even permutations.
Whether even permutations form a
subgroup of the permutation
group? Justify your answer. ​

Answer 1

The set of even permutations in Sn forms a subgroup of Sn. Proof. If α,β ∈ Sn and are both even, then αβ is also even since