1. Determine all possible non trivial subgroups of (Z4, +4) and find its left and right...

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1. Determine all possible non trivial subgroups of (Z4, +4) and find its left and right cosets. 2. Show that the mapping g: (Z4, +4) → (Zs", Xs), given by g([0])=[1], g([1])=[2], g([2])=[4] and g([3])=[3] is a homomorphism where Z5*-Zs -{[0]}. 1. Determine all possible non trivial subgroups of (Z4, +4) and find its left and right cosets. 2. Show that the mapping g: (Z4, +4) → (Zs", Xs), given by g([0])=[1], g([1])=[2], g([2])=[4] and g([3])=[3] is a homomorphism where Z5*-Zs -{[0]}.