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Math Help - group and identity help

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    group and identity help

    Suppose that (G, *) is a group, with identity e, where cardinality of G is even. Show that there must be an element g in G, with g not equal to e and g*g=e.
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    Quote Originally Posted by antoniowilliams46 View Post
    Suppose that (G, *) is a group, with identity e, where cardinality of G is even. Show that there must be an element g in G, with g not equal to e and g*g=e.
    If g\ne g^{-1} then (g^{-1})\ne (g^{-1})^{-1}. In other words the elements which aren't idempotent come in pairs.
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