For them a semigroup is by definition a non-empty set together with an associative binary operation.
[1][2] However not all authors insist on the underlying set of a semigroup being non-empty.
[3] One can logically define a semigroup in which the underlying set S is empty.
The binary operation in the semigroup is the empty function from S × S to S. This operation vacuously satisfies the closure and associativity axioms of a semigroup.
When a semigroup is defined to have additional structure, the issue may not arise.