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Direct Products of Groups

Let G=(x) x (y) where |x|=8 and |y|=4
a) Find all pairs a,b in G such that G=(a)x(b) (where a,b are expressed in terms of x and y)

b) Let H = (x^2)x(y^2) be isomorphic to (Z/4 x Z/2). Prove that there are no elements a,b of G such that G=(a)x(b) and H=(a^2) x (b^2)

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a) If G=(a)x(b), then |a|=8 and |b|=4. Since G=(x)x(y), then a is the power of x
and b is the power of y. Thus all ...

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Direct Products of Groups are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.