0
$\begingroup$

Let $G$ be a group and $$N:=\langle\{g^2:g\in G\}\rangle$$ Prove that $N$ is a normal subgroup.

I am quite not sure how to start on this exercise. I heard that this can be proven by using the notion of an index of a group but since we did not cover this in the lecture I think it should not be used. Has someone a hint for a more basic solution?

$\endgroup$
0

1 Answer 1

Reset to default
3
$\begingroup$

$x g^2 x^{-1} = (x g x^{-1}) (x g x^{-1}) = (x g x^{-1})^{2} \in N$.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged .