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

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 as usual. Calculate the cyclic polynomial Z_C4×C5 .

(b) Explain why in general Z_G×H = Z_GZ_H.

Expert Solution

Colby Messinger answered 1 year ago

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