Abstract Algebra
H is a subset of R x R
H := {(x,y) s.t. y = 2x}
Prove H is a normal subgroup of R x R.

Question

Abstract Algebra
H is a subset of R x R
H := {(x,y) s.t. y = 2x}
Prove H is a normal subgroup of R x R.

zzr0ck3r · Answer

I don't understand what the operation is
and if its multiplication if (x,y) is in H and (x',y') is in H
the y = 2x and y' = 2x' so yy' = 2*2xx' and thus not in H....

kinggeorge · Answer

Assuming R is the real numbers, the operation must be addition. Otherwise things go very badly with 0.

zzr0ck3r · Answer

right good call.

zzr0ck3r · Answer

so it would be the ordered pair (x+x',y+y')
and we would have y+y' = 2(x+x')?

kinggeorge · Answer

yes.

zzr0ck3r · Answer

and since R is commutative with addition H is a subgroup of an Abelian group and thus H is normal?

zzr0ck3r · Answer

every subgroup of an abelian group is normal.

kinggeorge · Answer

That would work.

zzr0ck3r · Answer

word. ty again kind sir:)

kinggeorge · Answer

You're welcome. Also, you still need to prove that it's a subgroup, but I assume you can handle that/already have.

zzr0ck3r · Answer

yeah for sure.