Question 156
a) Give an example of a finite nonabelian group $G$, with unit element $e$, having a proper subgroup $H$ with the property that $x^2 = e$ for any $x \in G \setminus H$.
b) Let $G$ be a finite group, and $H$ a proper subgroup such that $x^2 = e$ for any $x \in G \setminus H$. If $|G| \gt 2 \cdot |H|$, show that the group $G$ is commutative.
b) Let $G$ be a finite group, and $H$ a proper subgroup such that $x^2 = e$ for any $x \in G \setminus H$. If $|G| \gt 2 \cdot |H|$, show that the group $G$ is commutative.