Let $(G,*)$ be an abelian group with the identity $e$. An element $a\in G$ is called an idempotent if $\,a^2 = e\,$ (where $\,a^2 = a*a).\,$ Let $S = \{a \in G\mid a^2 = e\}.$
How do I prove $S$ is a subgroup of $G$?
Let $(G,*)$ be an abelian group with the identity $e$. An element $a\in G$ is called an idempotent if $\,a^2 = e\,$ (where $\,a^2 = a*a).\,$ Let $S = \{a \in G\mid a^2 = e\}.$
How do I prove $S$ is a subgroup of $G$?