# hw7 - G Z G(3 points 3 Prove that a group of order 1225 is...

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Math 4124 Monday, March 21 Seventh Homework Due 2:30 p.m., Monday March 28 1. Section 4.4, Exercise 3 on page 137. (If θ Aut ( D 8 ) , show θ ( r 2 ) = r 2 , and deduce θ ( s ) = r 2 .) (3 points) 2. Let G be a group. If Aut ( G ) is cyclic, prove that G is abelian. Hint: use Exercise 3.1.36 (ungraded HW Feb 9); what can you say about
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Unformatted text preview: G / Z ( G ) ? (3 points) 3. Prove that a group of order 1225 is abelian. (3 points) 4. Section 6.2, Exercise 3 on page 213. (3 points) (4 problems, 12 points altogether)...
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