Let P denote the multiplicative group of positive real numbers. Prove that {1} is the ONLY finite subgroup of P
@ikram002p group theory for you. Please help

Question

Let P denote the multiplicative group of positive real numbers. Prove that  {1} is the ONLY finite subgroup of P
@ikram002p  group theory for you. Please help

ikram002p · Answer

sorry i dont think i could help  with this

loser66 · Answer

It's ok, friend, hihihi... I still have my T.A in recitation tomorrow. No worried, it 's just homework. :)

anonymous · Answer

If $H$ were a subgroup of $P$, and $x\in H$, $x\ne 1$, then $x^n\in H$ for all $n\in \mathbb{N}$ since subgroups are closed under the group operation. 
Try to use this to show if you have a finite subgroup, the only element in the subgroup can be 1.

loser66 · Answer

Thanks a lot. I need you check my stuff, please.

loser66 · Answer

group size 3 : take off {0,7,21} , it is {0,7,14,21} belongs to group size 4