1. ## 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!

2. Originally Posted by alexandrabel90
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?