Aggression usually comes from (a) anxiety and (b) an escalation of warning people to back off because earlier signals have not been respected. For example, dogs give a series of signals that they are unhappy, but unfortunately most people don't recognise them because they can be quite subtle. To begin with there is often wide eyes, lip licking and yawning. There is also muscular tension in the body. Then the ones we sometimes do see - growl, snarl, nip then bite. If the early signals are not seen (or, in the dog's view, ignored) he won't bother with them because us stupid humans pay no attention anyway; so he may go straight to the bite. So it's important never to ignore the early signals or reprimand the dog for giving them; stopping the dog from giving them would be like taking the battery out of a smoke alarm.
And, I'm afraid alpha, dominance, pack leadership theory is plain wrong. It has been thoroughly disproven and widely discredited, even by the person who developed it. It was based on flawed conclusions drawn from poorly observed evidence. The wolf pack was not a real pack, it was a group of individuals thrown together and the situation (captivity rather than wild) skewed the data as their behaviour was not natural. And dogs are not wolves anyway, any more than we are chimpanzees - in both cases there was a shared ancestor but the species evolved in different directions. That's why we have humans AND apes, wolves AND dogs.
This article explains it quite well.
Debunking the "Alpha Dog" Theory - Whole Dog Journal
Nobody disagrees with boundaries and good manners, but the these can be established through training, building a mutually respectful relationship and without forcing submission from your dog. We certainly do not advocate aversive tools and behaviours.
If you think about leadership in your own life, the leaders (teachers , co-workers) that you respect
earn that respect and inspire followership, they don't command or force it through wielding power 'just because they can'.
So, I think just saying the dog is aggressive is looking at the outcome of many things that may have led up to this. How serious were the bites? Was skin broken? How often has it happened and under what circumstances?
If the bites were serious, it may be that you need more help than we can give online. But if you engage a behaviourist, please, for your dog's sake, find one who uses modern force free methods.