PMATH 336Due: June 9, 2020 at 9:00 AMAssignment 2 Comments1. (Xingchi) LetIbe the index set of nonzero real numbers and for everyα∈IletGαbe the group of nonzero complex numbers equipped with the operationa ? b=αab.ConsiderG=Yα∈IGα.(a) What is the identity ofG?
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(b) Considerf∈Ggiven byf(α) =α+i. What isf-1?
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(c) Letfbe as above and letg∈Gbe given byg(α) = 1 +αi. Computefg.
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2. (Aiden)(a) LetIbe a nonempty index set and for everyi∈IletGibe a group. SupposeHi≤Gifor everyi∈I. Prove thatYi∈IHi≤Yi∈IGi.1