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Groups and FieldsMediumNormal Subgroups and Quotient Groups

Normal Subgroups and Quotient Groups · Medium problem

Exactly one of these four maps φa:Z12→Z8\varphi_a: \mathbb Z_{12} \to \mathbb Z_8, k↦ak mod 8k \mapsto ak \bmod 8, fails to be a well-defined homomorphism (because φa(12)≠φa(0)\varphi_a(12) \ne \varphi_a(0)). Which value of aa is it?