Abstract algebra question

  • Thread starter Centurion1
  • Start date
  • #1
71
0
How many groups are there of order 7.

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

Thanks.
 

Answers and Replies

  • #2
1,097
3
Take a look at the group elements,

[tex] Z_{7} = \left\{ 1, a, a^{2},a^{3},a^{4},a^{5},a^{6}\right\}[/tex]
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,833
964
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
71
0
yes in hindsight this was such a duh answer.

it is one correct?
 
  • #5
1,097
3
it is one correct?

Correct.
 

Related Threads on Abstract algebra question

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
7
Views
5K
  • Last Post
Replies
5
Views
5K
  • Last Post
Replies
0
Views
963
  • Last Post
Replies
11
Views
2K
Replies
4
Views
5K
  • Last Post
Replies
1
Views
1K
Top