# Math Help - Finite Group Question

1. ## Finite Group Question

Let $G$ be a finite group and let $H\neq G$ be a subgroup of $G$. Show that $G\neq \cup_{a\in G} aHa^{-1}$.

2. Originally Posted by paulk
Let $G$ be a finite group and let $H\neq G$ be a subgroup of $G$. Show that $G\neq \cup_{a\in G} aHa^{-1}$.
3. Let $[G:H]=n\geq 2$. Then we have $|\cup_{a\in G} aHa^{-1}|\leq n(|H|-1)+1.