Question: 3. (a) Is union of two subgroups again a subgroup? Justify your answer. (b) Let G be a group and let a be a

3. (a) Is union of two subgroups again a subgroup? Justify your

3. (a) Is union of two subgroups again a subgroup? Justify your answer. (b) Let G be a group and let a be a fixed element of G. Show that C(a) {re G: ax = xa} is a subgroup of G. (c) Let f: G G be a group homomorphism. Define Kernel of f and show that it is a subgroup of G.

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