A subgroup \(H\) of a group \(G\) is normal if

A subgroup \(H\) of a group \(G\) is normal if

\(Hx=xH\) for some \(x\in G\)

\(Hx\neq xH\) for all \(x\in G\)

—>> \(H/xH\) for some \(x\in G\)

\(Hx=G\) for all \(x\in G\)

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