Does there exists a group $G$ and $H$ subgroup of $G$ such that there exists $g\in G$ with $gHg^{-1} \subseteq H$ but $gHg^{-1} \neq H$
I am unable to find an example and neither I am able to prove otherwise. Please help
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chesslad
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Order of conjugate subgroup is same as order of subgroup so can we conclude from that these are the same groups? – chesslad Feb 29 '20 at 23:33
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1No, we can't do that if the orders are infinite. – Arthur Feb 29 '20 at 23:37
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1You can find an example (necessarily infinite) here – Arturo Magidin Mar 01 '20 at 00:57