1. It is given that is a subgroup of GL2(Q). (a) Show that G= {(6) wit...

 

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1. It is given that is a subgroup of GL2(Q). (a) Show that G= {(6) wit N = = {(6) with a in (+1} and b in in Q} Now let : GS3 be a homomorphism. (c) Show that N< ker(). Hint: () = (1/6)6. (d) Determine the number of possible . with b in b in Q} is a normal subgroup of G and that there is an isomorphism G/N~ (±1). Hint: use the first isomorphism theorem. (b) Is it true that N = [G,G]? Hint: compute the commutator of some simple elements of G. 1. It is given that is a subgroup of GL2(Q). (a) Show that G= {(6) wit N = = {(6) with a in (+1} and b in in Q} Now let : GS3 be a homomorphism. (c) Show that N< ker(). Hint: () = (1/6)6. (d) Determine the number of possible . with b in b in Q} is a normal subgroup of G and that there is an isomorphism G/N~ (±1). Hint: use the first isomorphism theorem. (b) Is it true that N = [G,G]? Hint: compute the commutator of some simple elements of G.

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a To show that N is a normal subgroup of G we need to show that for any g in G and n in N the conjug... View the full answer