# Homework Help: Abstract algebra class equation

1. Mar 16, 2017

### Mr Davis 97

1. The problem statement, all variables and given/known
I
f each element of a group, G, has order
which is a power of p, then the order of G is also a prime power.

2. Relevant equations

3. The attempt at a solution
I am not sure really where to get started. I know that the class equation will be used though

2. Mar 16, 2017

### Staff: Mentor

How does your textbook define the phrase "order of a group"?

3. Mar 16, 2017

### Mr Davis 97

The order of G is the number of elements in G

4. Mar 16, 2017

### Staff: Mentor

And what is the order of an element of a group? It might be helpful to look at some examples, such as $(\mathbb{Z_4}, *)$ or $(\mathbb{Z_5}, *)$.

5. Mar 16, 2017

### Mr Davis 97

The order of an element of a group is the order of the cyclic subgroup that it generates.

6. Mar 16, 2017

### Dick

Sure it is. I suggest you apply Cauchy's theorem to your group. Suppose the order of $G$ is NOT a power of $p$?