On automorphism groups of idempotent evolution algebras

We study the automorphism group of an idempotent evolution algebra, show that any finite group can be the automorphism group of an evolution algebra, and describe certain evolution algebras with given automorphism groups. In particular, we classify n-dimensional idempotent evolution algebras whose automorphism group is isomorphic to the symmetric group Sn, and classify idempotent evolution algebras with maximal diagonal automorphism subgroups.