# Homework Help: Abstract algebra question

1. Jul 22, 2010

### Centurion1

How many groups are there of order 7.

I just need to know this to continue with an assignment.

Thanks.

2. Jul 22, 2010

### jegues

Take a look at the group elements,

$$Z_{7} = \left\{ 1, a, a^{2},a^{3},a^{4},a^{5},a^{6}\right\}$$

3. Jul 23, 2010

### HallsofIvy

The crucial point is that 7 is a prime number. How many subgroups can a group of order 7 have? What does that tell you?

4. Jul 23, 2010

### Centurion1

yes in hindsight this was such a duh answer.

it is one correct?

5. Jul 23, 2010

Correct.