**Unformatted text preview: **4.29 . Let S := { x ∈ G | x-1 6 = x } . Then S has an even number of elements because its elements can be grouped in pairs x, x-1 . 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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