(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

LetGbe a finite group andN[tex]\triangleleft[/tex]Gsuch that|N| = n, and gcd(n,[G:N]) = 1.

Proof that ifx[tex]^{n} = e[/tex]thenx[tex]\in[/tex]N.

2. Relevant equations

none.

3. The attempt at a solution

I defined |G| = m and and tried to find an integer which divides both n and m/n.

I went for some X which is not in N, for which X^n = e.

I defined o(X) = q and then q | n.

No luck showing that q | m/n.

Any other ideas?

Thanks ahead,

Zvi

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Quotient groups related problem

**Physics Forums | Science Articles, Homework Help, Discussion**