Recall that the center of a group G is the set Z(G)={x∈G:xg=gx for all g∈G}.

a. Calculate the center of S3.
b. Calculate the center of GL2(R).
c. Show that the center of any group G is a normal subgroup of G .
d. If G/Z(G) is cyclic, show that G is abelian.

Determine whether the question is a statistical question. explain. 1. what is the eye of sixth grade students? 2. at what temperature (in degree fahrenheit) does water freeze? 3. how many pages are in the favorite books of students your age? 4. how many hours do sixth grade students use the internet each week? you!