Groups with the subtraction operation Why do integer mod integer sets with the operation of subtraction not form groups?
For example, integers mod 3 is {0,1,2}, which has an identity (0) and inverses (self inverses). And subtraction is an operation because any arguments into the operation outputs something still within integers mod 3. I suspect I am missing something as to why that is not a group.

Have you checked associativity?
For example, is $(2-1)-1=2-(1-1)$?
