hw29 - : G K is an isomorphism. c. Show that the notion of...

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Intro to Abstract Math Homework 29 Fall 2009 Due December 4 Exercise 84. Show that Q and R (under addition) are not cyclic. [ Suggestion: Argue by contradiction. If a were a generator, what would need to be true about a/ 2?] Exercise 85. Let G , H and K be groups. a. Show that if ϕ : G H is an isomorphism, then ϕ - 1 : H G is an isomorphism. b. Show that if ϕ : G H and ψ : H K are isomorphisms, then
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Unformatted text preview: : G K is an isomorphism. c. Show that the notion of isomorphism is an equivalence relation on the collection of all groups. Exercise 86. Show that no two of Z 8 , U (16) and D 4 are isomorphic. Remember, the operation in Z 8 is addition mod 8, and the operation in U (16) is multiplication mod 16....
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