Modern Algebra Factor Groups question

[PsychonautQQ]

Homework Statement

If K is normal in G and |g| = n for some g in G, show that the order of Kg in G/K divides n.

Homework Equations

None

The Attempt at a Solution

Okay so I feel like I have a solution but I don't use all the information given so I'm trying to find holes in it...

g^n = 1

K = Kg^n = (Kg)^n. So it seems If we take Kg to the nth power we get it's identity. This means that the order of Kg must divide n.

What am I missing here?

 

[Dick]

Homework Statement

If K is normal in G and |g| = n for some g in G, show that the order of Kg in G/K divides n.

Homework Equations

None

The Attempt at a Solution

Okay so I feel like I have a solution but I don't use all the information given so I'm trying to find holes in it...

g^n = 1

K = Kg^n = (Kg)^n. So it seems If we take Kg to the nth power we get it's identity. This means that the order of Kg must divide n.

What am I missing here?

If you mean you aren't using that K is normal in G, you need that fact to justify saying (Kg)^n=Kg^n, or even that G/K is a group. Better review why.