Conjugation question

**Giraffro** · April 21st 2010, 03:18 AM

If $G$ is a group, $K \lhd G$ is proper and $\forall x \in G \backslash K, x^2 = e$ , show that $\forall t \in G \backslash K, \forall a \in K, t^{-1} at = a^{-1}$ .

I'm completely confused on how to solve this. I just seem to be going round in circles.

Can anyone help?

**Opalg** · April 21st 2010, 03:28 AM

Originally Posted by Giraffro

If $G$ is a group, $K \lhd G$ is proper and $\forall x \in G \backslash K, x^2 = e$ , show that $\forall t \in G \backslash K, \forall a \in K, t^{-1} at = a^{-1}$ .