Finite Order of Elements in Quotient Groups

[lorena82186]

Homework Statement

If G is a group and N is a normal subgroup of G, show that if a in G has finite order o(a), then Na in G/N has finite order m, where m divides o(a).

Homework Equations

The Attempt at a Solution

I have no idea where to start. The problem says to prove it by using the homomorphism of G onto G/N.

 

[antiemptyv]

Try taking a look at using Lagrange's Theorem.

 

[cmj1988]

I don't mean to dig this up, but isn't there a theorem (not sure if it lagrange) that states that the minimum order of an element to belong in a subgroup is a divisor of the group order. Couldn't one arrive at this by creating a bijection and then invoking the fact that |G:N|=|G|/|N|. <= That was something given to us in class that led to Lagrange's theorem.