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Unformatted text preview: 4.29 . Let S := { x G  x1 6 = x } . Then S has an even number of elements because its elements can be grouped in pairs x, x1 . Because G has an even number of elements, the number of elements in G but not in S (the set G \ S ) must be even. The set G \ S is nonempty because it contains e . Thus there is at least one element of G \ S other than e , that is, at least one element other than e that is its own inverse....
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 Fall '08
 OGUS
 Math, Algebra

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