Let G be a group acting on a set S, and let H be a group acting
on a set T. The product group G × H acts on the disjoint union S ∪
T as follows. For all g ∈ G, h ∈ H,
s ∈ S and t ∈ T,
(g, h) · s = g · s, (g, h) · t = h · t.
(a) Consider the groups G = C4, H = C5,
each acting...