Question

Abstract Algebra

Exercise 3.6.2 Let F be a field and let F = FU {o0) ( where oo is just a symbol). An F-linear fractional transformation is a function T: given by ar +b T(z) = cr + d ac). Prove that the set where ad-be 0 and T(oo) a/c, while T(-d/c) = o0 (recall that in a field, a/c of all linear fractional transformations M(F) is a subgroup of Sym(F). Further prove that if we let A < GL(2, F) denote the subgroup -KG % )) A then A is a normal subgroup and GL(2, F)/A M(F) In fact, A is the center of GL(2, F)

Answer both parts please.

Answer 1

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