Activity 4.4

The Center of a Group Every group contains certain important subsets, one of which is its center. Activity 4.4 Using the Cayley Table for the group of symmetries of the square (which we called as the Dihedral Group D4 where D4 = {1, R1, R2, R3,11,12,71,72), (a) The group D4 is not an Abelian group, but there are some elements in D4 that commute with all of the other elements. Find one such element. Are there any others? (b) Let Z(D4) be the set of all elements in De that commute with every element in D4. (i) Create a Cayley table for Z(DA) using the operation in D4. (ii) Is Z(Ds) a group? Explain.