1
$\begingroup$

I know very well that SL$(n,\mathbb{F})$ is a perfect group.

Can we say that it is simple and how can we find the non abelian square of GL$(n,\mathbb{R})$?

I have searched for these on google but did not get any affirmative result. Please help me.

$\endgroup$

1 Answer 1

1
$\begingroup$

No in general $SL(n,\mathbb{F})$ is not simple, suppose $\mathbb{F}=\mathbb{R}$ then it has non trivial center (https://en.wikipedia.org/wiki/SL2(R)). I think directly we can not say something about exterior square of $GL(n,\mathbb{R})$, but it will be an infinite group that contains $SL(n,\mathbb{R})$.

$\endgroup$
0

You must log in to answer this question.

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