hw25 - H is a subgroup of Aut( R ). [ Note: Remember that...

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Intro to Abstract Math Homework 25 Fall 2009 Due November 13 Exercise 72. Let G be an abelian group and let a,b G . Prove that ( ab ) n = a n b n for all n N . [ Hint: Use induction.] Exercise 73. Let H = { g : R R | g ( x ) = ax + b with a,b R and a 6 = 0 } . a. Prove that H Aut( R ). b. Prove that
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Unformatted text preview: H is a subgroup of Aut( R ). [ Note: Remember that the operation in Aut( R ) is composition.] Exercise 74. Let H and K be subgroups of a group G . Prove that H K is also a subgroup of G ....
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