Question 10
Let $p$ be an integer greater or equal to $2$ and let $(M, \cdot)$ be a finite semi-group, such that $a^p \neq a$, for all $a \in M \setminus \{e\}$, where $e$ is the null element in $M$. Prove that $(M, \cdot)$ is a group.
Traian Preda
Traian Preda