Consider G, a Domain which contains the one and a finite number of elements. Now Show that G is isomorphic to a field containing elements where q is a prime and n is a natural number.
A domain firstly means that G is a ring containing no left- or right- zerodivisors but the 0 itself. So intuitively if there is a number m that divides q there exists an element which can be multiplicated with q and since the characteristic of is q that has to be zero?
Yet I don't see a way to Show this in an understandable, formal correct way. Could please someone give me a hint what to do in this case here?