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Intr Abstract Alg I

by: Reuben Hudson DDS

Intr Abstract Alg I MATH 411

Reuben Hudson DDS
GPA 3.55


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Class Notes
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This 1 page Class Notes was uploaded by Reuben Hudson DDS on Friday October 30, 2015. The Class Notes belongs to MATH 411 at University of Massachusetts taught by Staff in Fall. Since its upload, it has received 24 views. For similar materials see /class/232230/math-411-university-of-massachusetts in Mathematics (M) at University of Massachusetts.

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Date Created: 10/30/15
H N3 03 4 U G 1 00 Math 411 Spring 2006 Review for exam 2 Format and Coverage You will be asked to give some de nitions7 proofs7 examples7 and counter examples The exam covers sections 147 21 7 257 317 32 excluding some material that we did not discuss in class The following is a practice exam7 which is also your homework for the week do not submit Give the de nition of a coset If G is a group and H is its subgroup prove that two cosets 1H and bH either do not intersect or coincide try to prove it Without looking at the textbooknotes Let f G a G be a group homomorphism Show that the order of an element a E G is divisible by the order of its image fa E G Does there exist a homomorphism g5 Z a Z3 gtlt Z2 that maps 2 to 17 1 Justify Let g5 Z9 a 33 be the unique homomorphism that maps 1 to the 3 cycle 123 Determine the kernel and the image of g5 Describe all possible onto homomorphisms from D4 to Z4 Let G be a group a Show that Q5 0 T9 TMQ o Z5 for any Z5 6 AutG and any 9 E G b Prove that InnG is a normal subgroup of AutG Show that V4 Z2 gtlt Z2 Bonus Prove that S4V4 Sg Hint There are three possible parti tions of the set 172374 into 2 element subsets a 172 U 3747 b 173 U 247 and c 174 U 273 Each permutation in S4 induces a permutation on the set 17 b7 c7 ie de nes an element of 83 Use the rst isomorphism theorem


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