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  3. let g be a group acting on a set s, and let h be a

Let G be a group acting on a set S, and let H be a...

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Advance Math

Let G be a group acting on a set S, and let H be a group actingon 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 as usual. Calculate the cyclic polynomialZC4×C5 .

(b) Explain why in general ZG×H =ZGZH.

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