MATH 311W Quiz: Math 311w quiz08
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Instructions: clearly answer each of the questions below. Remember to check the back side if blank, you can use it for scrap work. Show your work and any formulas you employ. In the problems below, assume that set g forms a group under the operation . Answer: to prove this is a group, we have to establish the 4 properties in the de nition of a group (see above). Function composition is always associative (see ch 2), so that is easy. e(z) acts as an identity, with e(z) = f (f (z) = g(g(z)) = h(h(z)), so each other function is it"s own inverse also. Find the cayley table for the subgroup hsi. Answer: the subgroup hsi = {[0]36, [9]36, [18]36, [27]36}. The cayley table is : the dihedral group d4 = hr, f i of sphereland symmetries of a square satis es r4 = f 2 = f rf r = e.
