Question: question 7 7. Let h be the function h : D5 - D10 where h(FRi) = FR2i and h(R.) = R2i for all i. (a)

question 7

7. Let h be the function h : D5 - D10 where h(FRi) = FR2i and h(R.) = R2i for all i. (a) Show that h is a one-to-one homomorphism. (b) Give the cardinalities | Dal, |Diol, and | Dio/ Dal. (c) Is h(D5) a normal subgroup? Hint: Recall that RF = FR-1. (d) Explain why {e, Ro } is a normal subgroup of Dio and write down an isomorphism D5 -+ Dio/{e, R'}. (e) Is Dio ~ D5 O C2? Explain

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