Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Suppose $G$ is a linear Lie group (i.e. $G$ admits a finite dimensional faithful representation) and $G$ has finitely many connected components. Let $G_0$ be the identity component of $G$. If $N$ is a normal subgroup of $G_0$, is $N$ necessarily normal in $G$?

share|improve this question
add comment

1 Answer

up vote 10 down vote accepted

No. Take $H$ to be a connected group, and $G=(\prod _{i=1}^n H)\rtimes S_n$. Where $S_n$ acts by permuting the factors. Then $G^0=\prod _{i-1}^n H$, and each of the factors $H$ is a normal subgroup in $G^0$ which is not normal in $G$.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.