Abstract algebra class equation

[Mr Davis 97]

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

Homework Equations

The Attempt at a Solution

I am not sure really where to get started. I know that the class equation will be used though

 

[Mark44]

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

Homework Equations

The Attempt at a Solution

I am not sure really where to get started. I know that the class equation will be used though

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

 

[Mr Davis 97]

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

The order of G is the number of elements in G

 

[Mark44]

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 $(\mathbb{Z_5}, *)$.

 

[Mr Davis 97]

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

 

[Dick]

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

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