Homework1 - conjugacy classes ) when G is the group of...

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Homework 1 Math 332, Spring 2010 These problems must be written up in L A T E X, and are due next Thursday. 1. Let G be a group. Two elements a,b G are said to be conjugate if there exists an element c G for which b = c - 1 ac . (a) Prove that “are conjugate” is an equivalence relation on G . (b) Determine the equivalence classes (known as
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Unformatted text preview: conjugacy classes ) when G is the group of symmetries of an equilateral triangle. (c) Determine the conjugacy classes when G is the group of symmetries of a square. 2. Let G be a group, and suppose that a 2 = e for every element a G . Prove that G is abelian. 1...
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