The left regular action is defined as follows: Let G be a group and A = G (as sets.) Define where g is any element of G and a is any element of A. ga is calculated using the group operation in G. The question is to find . The kernal in my text is defined as .

The only element I can come up with for the kernal is . That seems to little to me. Are there any others? A hint would be appreciated

Thanks.

-Dan