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Question: If $G$ is an infinite group, and $A, B$ subgroups of finite index in $G$, then prove $A \cap B$ has finite index in $G$.
I'm trying to show that $A\cap B$ can not have infinite index, but I can't make contradiction. I do not see where the problem in $A \cap B$ have infinite order comes from. I thought this look easy when I first saw it, but now I'm not so sure..I'm sure its true, but do not know where the contradiction comes from.
Thank you for help if you choose to help