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Groups and FieldsEasyNormal Subgroups and Quotient Groups

Normal Subgroups and Quotient Groups · Easy problem

In Z48\mathbb Z_{48}, let N=⟨24⟩N = \langle 24\rangle and K=⟨8⟩K = \langle 8\rangle, so N≤K≤Z48N \le K \le \mathbb Z_{48}. By the Third Isomorphism Theorem, (Z48/N)/(K/N)≅Z48/K(\mathbb Z_{48}/N)/(K/N) \cong \mathbb Z_{48}/K. What is ∣Z48/K∣|\mathbb Z_{48}/K|?