I wanted to post that DS was like this at thus age. I have a home communication book from nursery that included him pouring buckets of cold water on some children, hitting. fighting, scratching etc. Most days he would have at least one incident and often more and this was in 2.5 hour session!! He really was very very difficult to manage at nursery. In fact they allocated him a dedicated TA for 15 hours a week almost within a few weeks of him arriving in nursery . They were a brilliant nursery
We had similar problems with him at at home until about the age of 5 years old. At home we got rid of his aggressive behaviour towards other children and us by effectively removing him IMMEDIATELY from any situation where he hurt anyone. Funnily enough he found this very upsetting as he often wanted to play with other children, he just didn't know how and noisy crowded environments always led to him being over excited. We tried to avoid the things we worked out as triggers as well obviously but this didn't always work.
I remember one time at about 2.5 years old he was playing in a quiet sandpit. Another similar aged child came along and I started worrying as I could see signs that DS was a bit stressed so I went in and tried to distract him and to get him to play a bit less boisterously. He had been digging furiously and sand was flying around a bit which had been fine when there were no other children there but not so OK when the other child arrived. I was considering whether to remove him but wasn't keen as he hadn't actually done anything wrong yet and I knew he would really scream unless I gave him a warning about leaving .
The other parent thought I was being a bit OTT and said "oh he is fine. I could see she thought I was being too much of a helicopter parent. DS is an only and she had 3 children with her. I turned around to say to her, that he could be a bit unpredictable and before I finished my sentence he had hit the little girl over the head quite hard with a plastic spade.

I lost count of the times I left a park, play area or other "fun" activity carrying an absolutely screaming DS because he had hurt someone (I always warned him if it happened we would be leaving). He would often scream and cry for ages afterwards. Our technique was to get him to a safe place (the car, our home) and ignore the crying/screaming . We would stay with him and keep him safe but would absolutely not engage with him until he was calm.
After wards, when he was much calmer we would explain why he had had to leave. It took about a year but by the time he was 4-5 years old he had stopped his aggressive behaviour at home or when out with us completely. He still played boisterously and needed to run a lot but he didn't deliberately hurt people anymore
School was another matter he kept huting children there until about year 5 when it seemed to tail off completely. He is 11 years old now and has been in any trouble at school for hurting anyone for two years. His primary were really really good and worked with him a lot to get him to learn to control his aggression .
DS had a diagnosis of ASD and ADHD at 6 years old. I just wanted to explain all this so that people can see that this behaviour can change for children even those with ADS/ADHD but it often takes a LOT longer than you think it will. Also without a suportive school/nursery you will get nowhere.
For us DS only really behaved like this at school (after the age of about 5) so it was hard for us to do much except work with the school to encourage/support and yes sometimes to punish. It was incredibly difficult and stressful though and we had a lot of parents who were incredibly unhappy with us about it.
I very am proud of DS though . He has just started in year 7 at a mainstream school and is doing really well so far