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.

The pyraminx is a rubik's cube-type toy in the shape of a tetrahedron. the pyraminx shown below has edges 15\,\text{cm}15cm long and vertical height h=12.2\,\text{cm}h=12.2cm. the triangle drawn with dashed lines is a right triangle. what is the distance rr? round your answer to the nearest tenth.