Let SA be the group of all permutations of the set A, and let c be one particular element of A.
a. Show that {σ g SA | σ(c) = c}is a subgroup Sc,c of SA.
b. Let d ≠ c be another particular element of A. Is Sc,d= {σ ∈ SA | σ(c) = d} a subgroup of SA? Why or why not?
c. Characterize the set Sc,d of part (b) in terms of the subgroup Sc,c of part (a).
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