Using the Fundamental Theorem of Finitely Generated Abelian Groups, classify the following factor groups. (a) Z...
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Using the Fundamental Theorem of Finitely Generated Abelian Groups, classify the following factor groups. S (a) Z x Z/ < (5,6) > (b) Z3 x Z6/ < (1, 2) > (c) Z x Z/ < (4,4) > nto
ASAP
(1) (20 points) Using the Fundamental Theorem of Finitely Generated Abelian Groups, classify the following factor groups. (a) Z x Z/ < (5,6) > (b) Z3 x Z6/ < (1, 2) > (c) Zx Z/ < (4,4) >
(1) (20 points) Using the Fundamental Theorem of Finitely Generated Abelian Groups, classify the following factor groups. (a) ZxZ/ < (5,6) > (b) Zz Z6/ < (1,2) (0) ZxZ/ < (4,4) >
(1) (20 points) Using the Fundamental Theorem of Finitely Generated Abelian Groups, classify the following factor groups. (a) Z × Z / < ( 5 , 6 ) > (b) Z 3 × Z 6 / < ( 1 , 2 ) > (c) Z x Z / < (4, 4) >
Show all of your work for full credit. You must give valid reasons to be awarded full credit. (1) (20 points) Using the Fundamental Theorem of Finitely Generated Abelian Groups, classify the following factor groups. (a) Zx Z/ < (5,6) > (b) Zx x Z6/ < (1,2) > (c) ZxZ/ < (4,4) >
(a) State the Fundamental Theorem of Finitely Generated Abelian Groups. (b) List all abelian groups of order 2450 up to isomorphism. (c) Show every abelian group of order 2450 has an element of order 70.
Use the Fundamental Theorem of Finitely Generated Abelian Groups to answer the following: a. Find all abelian groups, up to isomorphism, of order p3 where p is a prime b. Use part (a) with a suitable p to list all possible abelian groups that are isomorphic to (Z2x From this list, identify the abelian group that is isomorphic to (Z2xZ8)/(1, 4))
(7)(20 points) (a) State the Fundamental Theorem of Finitely Generated Abelian Groups. (b) List all abelian groups of order 2450 up to isomorphism. (c) Show every abelian group of order 2450 has an element of order 70.
(7)(20 points) (a) State the Fundamental Theorem of Finitely Generated Abelian Groups. (b) List all abelian groups of order 2450 up to isomorphism. (c) Show every abelian group of order 2450 has an element of order 70.
In the problems below, give the
order of the element in the indicated
factor group.
(a) in
(b) in
(c) in
(5)(20 points) In the problems below, give the order of the element in the indicated factor group. (a) (1, 2)+ < (1,1) > in Z3 x Z6/ < (1,1) >. (b) (3, 2)+ < (4,4) > in Z6 * Z8/ < (4,4) >. (c) 26+ < 12 > in Z60/ <12>.