# Thread: Exam study guide help

1. ## Exam study guide help

For $\displaystyle H,K \leq G$ Set $\displaystyle H$~$\displaystyle K$ when for some $\displaystyle g \in G, K = g^{-1} Hg$
Finish the Statement: "|[$\displaystyle H$]_~| = 1 $\displaystyle \iff $$\displaystyle H is...." and justify your answer Thanks in advance... 2. Originally Posted by ElieWiesel This is of my final study guide, and Im confused by the question please help.... For \displaystyle H,K \leq G Set \displaystyle H~\displaystyle K when for some \displaystyle g \in G, K = g^{-1} Hg Finish the Statement: "|[\displaystyle H]_~| = 1 \displaystyle \iff$$\displaystyle H$ is...." and justify your answer
What does $\displaystyle \left|\left[H\right]_\sim\right|$ mean?
3. $\displaystyle \left|\left[H\right]_\sim\right|=1\iff \text{ for all } g\in G, H=g^{-1}Hg \iff H\text{ is normal subgroup of }G$