math 311w homework11 - 6. the set of integers under...

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Homework 11. Due Monday, April 26, 2010 Problem 1. Decide which of the following sets are groups under operation the given operations, explain your answer: 1. the set of rational numbers Q under multiplication; 2. the set of non–zero complex numbers C under multiplication; 3. the non–zero integers under multiplication; 4. the set of all functions from { 1 , 2 , 3 } to itself; 5. the set of real numbers of the form a + b 3 where a and b are integers under addition;
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Unformatted text preview: 6. the set of integers under subtraction; 7. the set of real numbers under the operation a * b = a + b + 2 Problem 2. Let G be a group and let c be a xed element of G . Dene a new operation * on G by a * b = ac-1 b Problem 3. Prove that there is at most one inverse element in a group. Problem 4. Let G be a group in which a 2 = e for all elements of G . Show that G is abelian. 1...
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This note was uploaded on 10/13/2010 for the course MATH 311W taught by Professor Mullen during the Spring '08 term at Pennsylvania State University, University Park.

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