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Math Help - groups

  1. #1
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    groups

    suppose that G is a group and let H={g is an element in G l g= inverse of g }. prove that if G is abelian then H is a subgrp of G.

    in ssuch a case, does it mean that if g is in G then inverse of g is in H.

    and if e is in G, then inverse of e is in H?

    i dont really get what does (g= inverse of g) in the criteria of H mean.

    thanks!
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by alexandrabel90 View Post
    suppose that G is a group and let H={g is an element in G l g= inverse of g }. prove that if G is abelian then H is a subgrp of G.

    in ssuch a case, does it mean that if g is in G then inverse of g is in H.

    and if e is in G, then inverse of e is in H?

    i dont really get what does (g= inverse of g) in the criteria of H mean.

    thanks!
    So H=\left\{g\in G:g=g^{-1}\right\}=\left\{g\in G:g^2=e\right\}. Does that clarify?
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