Nowhere commutative semigroup

A *nowhere commutative semigroup* is a type of algebraic structure characterized by its non-commutative nature. In algebra, a semigroup is defined as a set equipped with an associative binary operation. Specifically, a semigroup \( S \) is a set with a binary operation \( \cdot \) such that: 1. **Closure**: For all \( a, b \in S \), the product \( a \cdot b \in S \).