This image contains a task in Russian asking to select all correct statements about group automorphisms. Let me transcribe and analyze the content for you.

Task (translated): "Indicate all correct statements about group automorphisms."

Statements:

1. The group of automorphisms is always an abelian group.
2. The group of automorphisms can always be generated by one automorphism.
3. The identity element in the group of automorphisms is the identity automorphism.
4. Let $f$ and $g$ be automorphisms, then the following equality holds: $(f \circ g)(xy) = (f \circ g)(x)(f \circ g)(y)$
5. Under automorphism, only the identity element can map to the identity.
6. The set of automorphisms forms a group under the operation of composition.

Would you like me to verify the truth of each statement in detail?