Let Φ: G to H be a group homomorphism such that Φ(g) ≠ eH for some non-identity element g in G, where eH is the identity in group H. Furthermore, suppose that G has order 11 and that H has order 22. a) What are the possible orders of Φ(G)? Explain. b) Is Φ a one-to-one map? Explain. c) Prove that Φ(G) is a normal subgroup of H. Show your work.

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