Homework6 - G and H are groups prove that Z G × H = Z G ×...

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Homework 6 Math 332, Spring 2010 These problems must be written up in L A T E X, and are due this Thursday, March 18. 1. (a) If G and H are groups, prove that G × H H × G . (b) Let G and H be groups, and let A G and B H . Prove that A × B G × H . (c) Let G , G 0 , H , and H 0 be groups, and suppose that G G 0 and H H 0 . Prove that G × H G 0 × H 0 . (d) If
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Unformatted text preview: G and H are groups, prove that Z ( G × H ) = Z ( G ) × Z ( H ). 2. List the conjugacy classes in S 5 and determine the number of elements in each class. 3. Prove that there exist at least eight non-isomorphic groups of order 16....
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