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Math Help - GROUP problem please help??

  1. #1
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    GROUP problem please help??

    Let G be a group with a finite number of elements. Show that for any a in G, there exists an n in the positive integers such that a^n = e.

    The hint is to consider e, a, a^2, a^3, ...., a^m, and use the cancellation laws. Thanks
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by krohrs311 View Post
    Let G be a group with a finite number of elements. Show that for any a in G, there exists an n in the positive integers such that a^n = e.

    The hint is to consider e, a, a^2, a^3, ...., a^m, and use the cancellation laws. Thanks
    HINT: a^{m_1}=a^{m_2} for some m_1 \neq m_2 \in \mathbb{N}, because we are in a finite group.
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