What is the inverse of (2, 3) in Z3 X Z5?A. (1, 2)B. (2, 3)C. (3, 2)D. (2, 1)What is the order of (2, 3) in Z3 X Z5*?2364Find all abelian groups of order 64.A. Z64B. Z64,Z4 XZ16C. Z4 XZ16, Z4 X Z4 X Z4D. Z64,Z4 XZ16, Z4 XZ4 X Z4

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.1: Definition Of A Group

Problem 51E: Prove that the Cartesian product 24 is an abelian group with respect to the binary operation of...

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Prove that the Cartesian product 24 is an abelian group with respect to the binary operation of addition as defined in Example 11. (Sec. 3.4,27b, Sec. 5.1,53,) Example 11. Consider the additive groups 2 and 4. To avoid any unnecessary confusion we write [ a ]2 and [ a ]4 to designate elements in 2 and 4, respectively. The Cartesian product of 2 and 4 can be expressed as 24={ ([ a ]2,[ b ]4)[ a ]22,[ b ]44 } Sec. 3.4,27b 27. Prove or disprove that each of the following groups with addition as defined in Exercises 52 of section 3.1 is cyclic. a. 23 b. 24 Sec. 5.1,53 53. Rework Exercise 52 with the direct sum 24.
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What is the inverse of (2, 3) in Z3 X Z5*? A. (1, 2) B. (2, 3) C. (3, 2) D. (2, 1) What is the order of (2, 3) in Z3 X Z5*?

What is the inverse of (2, 3) in Z3 X Z5? A. (1, 2) B. (2, 3) C. (3, 2) D. (2, 1) What is the order of (2, 3) in Z3 X Z5?