aS=Sa
 

Let be S a subgroup of G


aS=Sa if for each s belonging to S exists a s' such that a*s=s' * a and for each s there is a s'' such that s*a=a*s''


The first condition a*s=s'*a means that aS<=Sa?


so the elements of aS could be lesser than the elements of Sa. This because the mapping is surjective?


suppose we have S=(s1,s2,s3,s4)


the elements of aS could be s1a=s2a=as3...so in aS there are only three elements whereas in Sa there are four elements?