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
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 $\displaystyle \frac{n!}{2}$.Originally Posted by mathlg
In this case $\displaystyle n=4$ thus,
$\displaystyle \frac{4!}{2}=\frac{24}{2}=12$
Thus there are 12 even premutations.
For the second part, all the premutations you named are odd!
Because,
$\displaystyle (a,b,c,d)=(a,b)(b,c)(c,d)$
The number of transpositions here is an odd number!
Also, the premutation
$\displaystyle (a,b,c,d)=(d,a,b,c)$
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.