Section 5.2
Cycles
Let g
be a permutation of Sn.
Associated to g are the points which are moved and
the points which are fixed by g.
Definition
The fixed points of g are the elements of {1, ..., n} for which g(i) = i holds. We denote the set of all fixed points of g by fix(g).
The support supp(g) of g is the complement in X of fix(g).
If g(x) = x, i.e., x is a fixed point of g,
then we say that x is fixed
by g. If g(x) 
x, i.e.,
x is in the support of g, we say that g moves x.