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Abstract algebra question

  • Thread starter Centurion1
  • Start date
  • #1
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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
2
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
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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
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yes in hindsight this was such a duh answer.

it is one correct?
 
  • #5
1,097
2
it is one correct?
Correct.
 

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