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If $G$ is a virtually abelian group and $H$ is a finite index subgroup of $G$. Is it always true that $H$ is virtually abelian ?

Since $G$ is V.A, it has a finite index subgroup $K$ which is abelian.

If $H \subset K$, then $H$ is abelian and therefore V.A.

If $K \subset H$, then $H$ is V.A.

What about when neither subgroup is contained in the other ?

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    Can you say something about $K \cap H$?2011-08-22
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    @user463498: I've merged your account with the account named "Seth" (unfortunately it was impossible to do the other way around). Because [you can only comment on your own questions, your own answers, and answers to your own questions](http://meta.stackexchange.com/questions/19756/how-do-comments-work/19757#19757) when you have $\leq 50$ reputation points, you were unable to comment on Arturo's answer because this question was owned by the account "Seth". If you have trouble logging in in the future, comment or leave a "flag" for moderator help.2011-08-30

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