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Groups and FieldsMediumNormal Subgroups and Quotient Groups

Normal Subgroups and Quotient Groups · Medium problem

Both φ9(k)=9k mod 18\varphi_9(k) = 9k \bmod 18 and φ12(k)=12k mod 18\varphi_{12}(k) = 12k \bmod 18 are valid homomorphisms Z24→Z18\mathbb Z_{24} \to \mathbb Z_{18}. Which has the LARGER kernel, and how many elements does that kernel have?