The definition of a normal subgroup is: for each element,n, inNand eachginG, the elementgng−1 is still inN where N is a subgroup of G.Can this be changed to ...element g−1ng is still in N.I think it still makes sense since gng−1=m for some m in N thus g−1gng−1g=g−1mg which gives n=g−1mg . Now g−1mg is in N since n is in N.

Is this correct?