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Groups and FieldsHardNormal Subgroups and Quotient Groups

Normal Subgroups and Quotient Groups · Hard problem

The special linear group SL(2,Z7)SL(2,\mathbb Z_7) is the kernel of the determinant map det⁡:GL(2,Z7)→U(7)\det: GL(2,\mathbb Z_7) \to U(7) (units mod 77 under multiplication). Use the first isomorphism theorem to find ∣SL(2,Z7)∣|SL(2,\mathbb Z_7)|.