Let G be a group. Let the centralixer C(X), X a subset of G, be defined as follows: C(X)={g in G | gx=xg for all x in X}.
Prove the following:
If X is a subset of Y, then C(Y) is a subset of C(X)
X is a subset of C(C(X))
C(X) = C(C(C(X)))
Let G be a group. Let the centralixer C(X), X a subset of G, be defined as follows: C(X)={g in G | gx=xg for all x in X}.
Prove the following:
If X is a subset of Y, then C(Y) is a subset of C(X)
X is a subset of C(C(X))
C(X) = C(C(C(X)))