- #1

- 8

- 0

## Homework Statement

Let G be a finite group and K a normal subgroup of G

If |K|=p where p is a prime

Prove that |G/C

_{G}(K)| divides p-1

## Homework Equations

## The Attempt at a Solution

I must show that |G| / |C

_{G}(K)| * something = p-1

I figured a good place to start would be to determine the cardinality of C

_{G}(K) which I'm having trouble with.

So I just started writing down things that would help

Since K normal in G => N

_{G}(K)=G

and since C

_{G}(K) is normal in N

_{G}(K) => C

_{G}(K) is normal in G