Are computer integers a finite group (under addition with overflow)?

The integers and the integers modulo a prime are both groups under addition.

What about the computer representation of integers (e.g. int64)?

It's closed under addition, since a sum that is too large wraps around to the negatives. It also inherits the other group properties from the integers (associativity, identity, inverse).

So int64 seems like a finite group, but am I missing anything?

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