groups

Aug 2009
639
2
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!
 

Drexel28

MHF Hall of Honor
Nov 2009
4,563
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Berkeley, California
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 \(\displaystyle H=\left\{g\in G:g=g^{-1}\right\}=\left\{g\in G:g^2=e\right\}\). Does that clarify?
 
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