| Line 5: | Line 5: | ||
What do the elements of D12 and S4 look like? I found some pictures of what D12 and S4 can look like, but I am really stuck on what the elements are. Are they the rotations and reflections? -[[-Josie]] | What do the elements of D12 and S4 look like? I found some pictures of what D12 and S4 can look like, but I am really stuck on what the elements are. Are they the rotations and reflections? -[[-Josie]] | ||
| + | |||
| + | [[Category:MA453Spring2009Walther]] | ||
| + | |||
| + | Yes they are the rotations and reflections. There are 12 rotations (30 degrees each - 360/12) as well as reflections. So you can see that D12 has elements of order 12 from those rotations and reflections. Then in S4 you either have a 4-cycle, or a 3-cycle, or 2 2-cycles, or 1 2-cycle. The orders of these are 4, 3, 2, 2. So none of them are order 12. | ||
| + | |||
| + | --[[User:Nswitzer|Nswitzer]] 16:37, 10 February 2009 (UTC) | ||
Revision as of 12:37, 10 February 2009
Prove that S4 is not isomorphic to D12.
D12 has elements of order 12 whereas S4 does not and therefore they cannot be isomporphic. --Aifrank 17:05, 9 February 2009 (UTC)
What do the elements of D12 and S4 look like? I found some pictures of what D12 and S4 can look like, but I am really stuck on what the elements are. Are they the rotations and reflections? --Josie
Yes they are the rotations and reflections. There are 12 rotations (30 degrees each - 360/12) as well as reflections. So you can see that D12 has elements of order 12 from those rotations and reflections. Then in S4 you either have a 4-cycle, or a 3-cycle, or 2 2-cycles, or 1 2-cycle. The orders of these are 4, 3, 2, 2. So none of them are order 12.
--Nswitzer 16:37, 10 February 2009 (UTC)
