4200t3 - Math 4200 Section 2/ Fall 2002 Name: Test 3 Please...

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Math 4200 Section 2/ Fall 2002 Test 3 Name: Please provide full explanations with your answers. No credit will be given for an answer which is not explained. Your work must be presented in a clean and formal way. 1. Suppose H and K are finite subgroups of a group G such that | H | and | K | are coprime. Prove that H K = { e } , where e is the identity element in G . (10pts)
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2. Write out all the six elements of S 3 and then write out all possible subgroups of S 3 . (10pts)
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3. Recall that for any integer m , we have the quotient Z m = Z /m Z which is a group
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4200t3 - Math 4200 Section 2/ Fall 2002 Name: Test 3 Please...

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