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Groups and FieldsEasyNormal Subgroups and Quotient Groups

Normal Subgroups and Quotient Groups · Easy problem

Let φ:Z12→Z8\varphi: \mathbb Z_{12} \to \mathbb Z_8 send k↦2k mod 8k \mapsto 2k \bmod 8. By the First Isomorphism Theorem, Z12/ker⁡φ≅im⁡φ\mathbb Z_{12}/\ker\varphi \cong \operatorname{im}\varphi. What is ∣Z12/ker⁡φ∣|\mathbb Z_{12}/\ker\varphi|?