How many groups are there of order 7?

[Centurion1]

How many groups are there of order 7.

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

Thanks.

 

[jegues]

Take a look at the group elements,

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

 

[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?

 

[Centurion1]

yes in hindsight this was such a duh answer.

it is one correct?

 

[jegues]

it is one correct?

Correct.