zzr0ck3r
  • zzr0ck3r
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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zzr0ck3r
  • zzr0ck3r
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
  • KingGeorge
Assuming R is the real numbers, the operation must be addition. Otherwise things go very badly with 0.
zzr0ck3r
  • zzr0ck3r
right good call.

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zzr0ck3r
  • zzr0ck3r
so it would be the ordered pair (x+x',y+y') and we would have y+y' = 2(x+x')?
KingGeorge
  • KingGeorge
yes.
zzr0ck3r
  • zzr0ck3r
and since R is commutative with addition H is a subgroup of an Abelian group and thus H is normal?
zzr0ck3r
  • zzr0ck3r
every subgroup of an abelian group is normal.
KingGeorge
  • KingGeorge
That would work.
zzr0ck3r
  • zzr0ck3r
word. ty again kind sir:)
KingGeorge
  • KingGeorge
You're welcome. Also, you still need to prove that it's a subgroup, but I assume you can handle that/already have.
zzr0ck3r
  • zzr0ck3r
yeah for sure.

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