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Groups and FieldsEasyNormal Subgroups and Quotient Groups

Normal Subgroups and Quotient Groups · Easy problem

Let φ:Z15→Z9\varphi: \mathbb Z_{15} \to \mathbb Z_9 send k↦3k mod 9k \mapsto 3k \bmod 9. By the First Isomorphism Theorem, ∣Z15/ker⁡φ∣=∣im⁡φ∣|\mathbb Z_{15}/\ker\varphi| = |\operatorname{im}\varphi|. What is this common value?