Let $H$ be a subgroup of a group $G$. If for each $a \in G$, there exists $b \in G$ such that $aH = Hb$, then prove that $H$ is a normal subgroup of $G$. How do I proceed?
2026-04-01 17:36:52.1775065012
Prove that $H$ is a normal subgroup of $G$. [$aH =Hb$]
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If $aH=Hb$ then $a\in Hb$ so $a=hb$ then $Hb=H(hb)=Ha$. Hence, $aH=Ha$.