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Consider the group G = Z4 X Z9 where the operation is done componentwise, that is (a, b) * (c,d) = (a +4 c, b +9 d), V(a, b), (c,d) E G. (a) Find the elements of the subgroup ((2,3)). (b) Compute [G : ((2,3))]. (c) Find the elements of the left coset (2, 1) + ((2, 3)).

Consider the group G = Z4 X Z9 where the operation is done componentwise, that is (a, b) * (c,d) = (a +4 c, b +9 d), V(a, b), (c,d) E G. (a) Find the elements of the subgroup ((2,3)). (b) Compute [G : ((2,3))]. (c) Find the elements of the left coset (2, 1) + ((2, 3)).

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.5: Isomorphisms
Problem 8E: Exercises 8. Find an isomorphism from the group in Example of this section to the multiplicative...
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Consider the group G = Z4 X Z9 where the operation is done componentwise, that is (a, b) * (c,d) = (a +4 c, b +9 d), V(a, b), (c,d) E G. (a) Find the elements of the subgroup ((2,3)). (b) Compute [G : ((2,3))]. (c) Find the elements of the left coset (2, 1) + ((2, 3)).
Transcribed Image Text:Consider the group G = Z4 X Z9 where the operation is done componentwise, that is (a, b) * (c,d) = (a +4 c, b +9 d), V(a, b), (c,d) E G. (a) Find the elements of the subgroup ((2,3)). (b) Compute [G : ((2,3))]. (c) Find the elements of the left coset (2, 1) + ((2, 3)).
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