aS=Sa

enzocreti · 2019-08-01, 13:37

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?

2019-08-01, 13:37	#1
enzocreti Mar 2018 2×5×53 Posts	aS=Sa Let be S a subgroup of G aS=Sa if for each s belonging to S exists a s' such that as=s' a and for each s there is a s'' such that sa=as'' The first condition as=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? Last fiddled with by enzocreti on 2019-08-02 at 05:35