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Groups and FieldsMediumNormal Subgroups and Quotient Groups

Normal Subgroups and Quotient Groups · Medium problem

In Z40\mathbb Z_{40}, let H=⟨8⟩H = \langle8\rangle and N=⟨4⟩N = \langle4\rangle. Since every multiple of 88 is automatically a multiple of 44, HH sits entirely inside NN. What is ∣H∩N∣|H \cap N|?