Hi Jennifer,
Please don't panic ! Your child is having to deal with lots of other children, when she is used to one to one attention. She is porbably trying to assert herself and is learning to deal with the other children. If she has just started nursery, it is ry early days. It is important for her to socialise.... she's just having to learn a lot all at once.
My youngest used to be violent towards other children (usually only her siblings). She is a strong character and she has learned other ways to make her presence be felt now. She is 9, and when I go to parents evenings, I am now told she is a delight to have in class. Your daughter is in a completely new environment, she is young and she is probably trying to find where the boundaries are. I am sure she will find the boundaries at nursery quickly and this behaviourwill stop. Just make sure if you ever see her being rough, you tell her firmly no. If my daughter ever got hurt by another child, I used that as an opportunity to say 'It asn't nice that XXXXX hit you, and it hurts, doesn't it. She shouldn't have done that to you... but how you feel now is how YYYY felt when you hit her. That wasn't nice either'. At 3, she is too young to completely grasp what your saying, but eventually they understand.

Good luck... and don't worry... it doesn't mean she'l always be like this!!!