The set of integers includes negative integers as well as positive integers.
It also includes the number zero which is neither negative nor positive.
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No.
The answer below is incomplete.The set of whole numbers also includes all negative integers.
The set of positive integers does not contain the additive inverses of all but the identity. It is, therefore, not a group.
The "integers of 15" appear to be '1' and '5'. Their product is 5 .
The set of positive integers, of course!