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.

Answer 1

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....

Answer 2

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

Answer 3

right good call.

Answer 4

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

Answer 5

yes.

Answer 6

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

Answer 7

every subgroup of an abelian group is normal.

Answer 8

That would work.

Answer 9

word. ty again kind sir:)

Answer 10

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

Answer 11

yeah for sure.