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Math Help - Element of a Group

  1. #1
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    Element of a Group

    Let G be a finite group. Prove that if \mid G \mid is odd then every element in g \in G can be expressed as g=x^2 for some x \in G.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by Markeur View Post
    Let G be a finite group. Prove that if \mid G \mid is odd then every element in g \in G can be expressed as g=x^2 for some x \in G.
    Use the pigeon-hole principle. This can be used as x^2 \neq 1 for x \neq 1, because the order of an element must divide the order of the group, so no element can have order 2.
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