C5. automorphism by conjugtion Consider the following automorphism of S4 defined by conjugation by the element (12): (p

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C5. automorphism by conjugtion
Consider the following automorphism of S4 defined by conjugation by the element (12):
(phi)_(23): S4 -> S4
p |-> (23) p (23)
a) Find the image of each of the following
b) Verify this is an automorphism
c) What are the fixed points of (phi)_(23)?
(i.e. Find the elements of {x in S4 : (phi)_(23) (x) = x}, i.e. (23) x (23) = x).
C5. automorphism by conjugtion
Consider the following automorphism of S4 defined by conjugation by the element (12):
(phi)_(23): S4 -> S4
p |-> (23) p (23)
a) Verify this is an automorphism
b) What are the fixed points of (phi)_(23)?
(i.e. Find the elements of {x in S4 : (phi)_(23) (x) = x}, i.e. (23) x (23) = x).