I am having a little touble with finite fields at the moment. I am just working from a high school text wich says that the inverse of an element in a group is unique, which to me implies that all elements have an inverse. But when I look a any multiplicative group $F_2$, the zero $0$ element never has an inverse?
I was wondering if I have something wrong or is zero special? Or is the theorem wrong? The thing that worries me is that if I treated groups abstractly, with symbols rahter than numbers, then 0 would look very strange, i.e. what would zero correlate isomorphically with symetries?
I think I should know this.