Consider Cayley digraphs with two are types, a solid one with an arrow and a dashed one wi...

Consider Cayley digraphs with two are types, a solid one with an arrow and a dashed one with no arrow, and consisting of two regular n-gons, for n ≥ 3, with solid are sides, one inside the other, with dashed arcs joining the vertices of the outer n-gon to the inner one. Figure 7.9(b) shows such a Cayley digraph with n = 3, and Figure shows one with n = 4. The arrows on the outer n-gon may have the same (clockwise or counter clockwise) direction as those on the inner n-gon, or they may have the opposite direction. Let G be a group with such a Cayley digraph.

a. Under what circumstances will G be abelian?

b. If G is abelian, to what familiar group is it isomorphic?

c. If G is abelian, under what circumstances is it cyclic?

d. If G is not abelian, to what group we have discussed is it isomorphic? Concepts