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Solve groups and proofs

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1.) Show that Z(II_alpha G_alpha)=II_alpha Z(G_alpha)

2.) Show that (G_1 x G_2 x ... x G_n)' = G'_1 x G'_2 x ... x G'_n

3.) Under what circumstances is G_1 x G_2 x ... x G_n solvable?

Note that II_alpha is the product over all alpha of an index set.

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Solution Summary

This provides examples of working with solvable groups.

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