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Test2_Practice_Sp10

Test2_Practice_Sp10 - Math 3330 Spring 2010 Test 2 Practice...

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Math 3330 Spring 2010 Test 2 Practice Problems 1. Prove or disprove whether the set :b is odd a GQ b =∈ ⎩⎭ with addition is a group. You may assume that addition is associative, you must justify ALL other claims. 2. Is the set of all real numbers x such that 01 x < with the operation of multiplication a subgroup of the group of all nonzero real numbers with multiplication? Justify your answer. 3. Let G be the group of complex numbers under addition. Define a map : G γ ] by () nn i = . a). Prove or disprove that is a homomorphism. b). Is the map onto? c). Is the map one-to-one? d). Is it an isomorphism? e). Find the kernel. 4. Given the group of invertible 2x2 matrices with real number entries with multiplication, is the set G :, , 0 0 ab Ha b a a ⎧⎫ ⎛⎞ ⎨⎬ ⎜⎟ ⎝⎠ ] a subgroup of G. 5. Cyclic groups - Consider the group with addition. 12 ] a). Find 7 b). Find 4 c). What is the order of the element [9]? d). Does have a subgroup of order 5?

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Test2_Practice_Sp10 - Math 3330 Spring 2010 Test 2 Practice...

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