Thread: Permutations (Want to check my answer)

I just want to make sure my answer is correct


Questions: List all even permutations of symmetry group S4


Answer: There are 12 even permutations in S4
(1234)(1342)(1423)(2143)(3124)(4132)(2431)(2314)(4 213)(3241)(3412)(4321)


Please Help

Originally Posted by mathlg

I just want to make sure my answer is correct


Questions: List all even permutations of symmetry group S4


Answer: There are 12 even permutations in S4
(1234)(1342)(1423)(2143)(3124)(4132)(2431)(2314)(4 213)(3241)(3412)(4321)


Please Help

Rememeber that the cardinality of the finite 'alternating group" is .
In this case thus,

Thus there are 12 even premutations.

For the second part, all the premutations you named are odd!
Because,

The number of transpositions here is an odd number!
Also, the premutation


Thus, there are two mistakes, first they are all odd

and not all are distinct-which basically means you did not list all the odd premutations.

A4 = {(1,2,3), (1,3,2), (1,2,4), (1,4,2), (1,3,4), (1,4,3), (2,3,4), (2,4,3), (1,2)(3,4), (1,3)(2,4), (1,4)(2,3),e}.