• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Showing Subgroups of a Permutation Group are Isomorphic

  • Thread starter Obraz35
  • Start date
Define two subgroups of S6:
G=[e, (123), (123)(456)]
H=[e, (14), (123)(456)]

Determine whether G and H are isomorphic.

It seems as if they should be since they have the same cardinality and you can certainly map the elements to one another, but I don't know what other factors need to be considered when deciding whether they are isomorphic.
 
H is not a subgroup since (14)(123)(456) = (123456) which is not in H. Are you sure you've written down the correct group?
 
Oops. I meant G=<(123), (123)(456)> and H=<(14), (123)(456)>.
 

Related Threads for: Showing Subgroups of a Permutation Group are Isomorphic

Replies
2
Views
687
Replies
1
Views
1K
Replies
6
Views
2K
Replies
4
Views
3K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top