Thread: Groups problem...(Axioms)

Say S is a set of elements (finitely or infinetly). Suppose that S is closed under the operation *, and that the associative law holds. If a*e=a and there exists -a (the inverse element) such that a*(-a)=e for all a in S. Then e*a=a and (-a)*a=e and the uniqueness of e (the identity element) can be deducted.


A little help with this is needed. Thanks in advance.

Originally Posted by Kichigo

Say S is a set of elements (finitely or infinetly). Suppose that S is closed under the operation *, and that the associative law holds. If a*e=a and there exists -a (the inverse element) such that a*(-a)=e for all a in S. Then e*a=a and (-a)*a=e and the uniqueness of e (the identity element) can be deducted.


A little help with this is needed. Thanks in advance.

First prove that in , and then prove that (it seems to be that is more usual and clearer to denote the inverse of than ).
Finally, use the above to prove

Tonio