Finding Subgroups of certain orders

  • Thread starter RVP91
  • Start date
  • #1
50
0
I'm not sure how for example I would go about finding the subgroups of S_4 of order 4?

I don't quite understand how I would I find or construct subgroups for a permutation group?

Any advice?

Thanks
 

Answers and Replies

  • #2
lavinia
Science Advisor
Gold Member
3,238
625
I'm not sure how for example I would go about finding the subgroups of S_4 of order 4?

I don't quite understand how I would I find or construct subgroups for a permutation group?

Any advice?

Thanks
1 ->2 ->3 ->4 ->1
1 ->3 ->2 ->4 ->1 for example
 
  • #3
jgens
Gold Member
1,581
50
Suppose [itex]\sigma \in S_n[/itex] is a 4-cycle. What can you say about [itex]\langle \sigma \rangle[/itex]?
 
  • #4
50
0
After using both your advice I think I have made some progress.

I used (1 2 3 4) and generated a subgroup of order 4, this subgroup was, {id, (1234), (13)(24), (1432)}, is this correct? And this is of order 4 so meets the condition.
I also did the same with (1324).

After reading a theorem I concluded if I want the subgroups to be of order 4 then the elements of the subgroups must divide 4. So since I've done the two for 4 would I know need to do the same for elements of order 2? Is there a shortcut or do I have to compute them all to check they form subgroups of order 4?

After attempting this with for example (12)(34) I found the usual method of multiplying by itself to try and find a group quickly failed since (12)(34)(12)(34) is simply id.

How do I find the subgroups using elements of order 2?

Thanks for the previous advice and an advance thanks for anymore
 

Related Threads on Finding Subgroups of certain orders

  • Last Post
Replies
8
Views
4K
Replies
1
Views
2K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
3
Views
759
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
1
Views
792
Replies
8
Views
2K
  • Last Post
2
Replies
33
Views
3K
Top