# Abstract algebra question

How many groups are there of order 7.

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

Thanks.

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Take a look at the group elements,

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

HallsofIvy
Homework Helper
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?

yes in hindsight this was such a duh answer.

it is one correct?

it is one correct?
Correct.