# Thread: Exam study guide help

1. ## Exam study guide help

This is of my final study guide, and Im confused by the question please help....

For $H,K \leq G$ Set $H$~ $K$ when for some $g \in G, K = g^{-1} Hg$

Finish the Statement: "|[ $H$]_~| = 1 $\iff$ $H$ is...." and justify your answer

2. Originally Posted by ElieWiesel
This is of my final study guide, and Im confused by the question please help....

For $H,K \leq G$ Set $H$~ $K$ when for some $g \in G, K = g^{-1} Hg$

Finish the Statement: "|[ $H$]_~| = 1 $\iff$ $H$ is...." and justify your answer

What does $\left|\left[H\right]_\sim\right|$ mean?
3. $\left|\left[H\right]_\sim\right|=1\iff \text{ for all } g\in G, H=g^{-1}Hg \iff H\text{ is normal subgroup of }G$