Answer: indirect object
Step-by-step explanation:
From the sentence "Sylvia bought her mother a beautiful necklace on her birthday", mother is an indirect object.
We can see that even though"mother" isn't the direct object which in this case is the necklace, she is the indirect object as the mother will be the one to receive the necklace. She is affected by the action that occurs in the sentence as she is the recipient.