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Math Help - Odd order group

  1. #1
    Newbie Sorombo's Avatar
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    Odd order group

    Let be G a group of order 2n-1. Show that there's no element in G that is its own inverse.
    Last edited by Sorombo; June 1st 2012 at 05:40 PM.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Odd order group

    Suppose there's an element in G of order 2n-1 that is it's own inverse and try to prove it's a contradiction.
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  3. #3
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    Re: Odd order group

    by a corollary to lagrange, the order of an element divides the order of G. if an element is it's own inverse, it is either the identity, or of order 2.

    as you have stated your problem, the statement is false, since EVERY group contains an identity element, which is ALWAYS it's own inverse.

    what IS true, is that every non-identity element of a group of order 2n-1 cannot be its own inverse.

    because 2n-1 is odd, and 2 does not divide an odd number.
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