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  1. #1
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    if G is a finite group, does it mean that there wil always be an element g in G where g^k= e, and k is the order if G? or it might not always be the case?
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    if G is a finite group, does it mean that there wil always be an element g in G where g^k= e, and k is the order if G? or it might not always be the case?

    If a group G is finite of order k then g^k=e for all elements g\in G...this follows at once from Lagrange's theorem.
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by tonio View Post
    If a group G is finite of order k then g^k=e for all elements g\in G...this follows at once from Lagrange's theorem.
    I think (or hope) that he meant does it follow there is an element of G whose order is the same as the group. The answer is clearly no by considering any non-cyclic group.
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