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(a) Consider (3,6) and (2,4) as elements of Z7xZ7. Compute (3,6) - (2,4). (b) Consider (3,6) and (2,4) as elements of R* x Z10. Compute (3,6)-(2,4).

(a) Consider (3,6) and (2,4) as elements of Z7xZ7. Compute (3,6) - (2,4). (b) Consider (3,6) and (2,4) as elements of R* x Z10. Compute (3,6)-(2,4).

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.4: Cosets Of A Subgroup
Problem 24E: Find two groups of order 6 that are not isomorphic.
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Please do Exercise 15.2.13 part ABC and please show step by step and explain

Definition 15.2.12. Given two groups G and H, we define the product of groups G and H (denoted by GxH) as the set of pairs {(g, h), g = G, h = H}. If (gi, hi) and (g2, h2) are two elements of G x H, then we define the group operation (gi, h₁) o (92, h₂) as follows: (91, h₁) (92, h₂) : (9192, h₂h₂), where gig2 uses the group operation in G and hih2 uses the group operation in H. Exercise 15.2.13. (a) Consider (3,6) and (2, 4) as elements of ZxZ7. Compute (3,6) (2, 4). (b) Consider (3,6) and (2, 4) as elements of R*x Z10. Compute (3,6)-(2,4). 506 CHAPTER 15 INTRODUCTION TO GROUPS (c) Consider (3,6) and (2,4) as elements of Q*x Q. Compute (3,6)-(2,4).
Transcribed Image Text:Definition 15.2.12. Given two groups G and H, we define the product of groups G and H (denoted by GxH) as the set of pairs {(g, h), g = G, h = H}. If (gi, hi) and (g2, h2) are two elements of G x H, then we define the group operation (gi, h₁) o (92, h₂) as follows: (91, h₁) (92, h₂) : (9192, h₂h₂), where gig2 uses the group operation in G and hih2 uses the group operation in H. Exercise 15.2.13. (a) Consider (3,6) and (2, 4) as elements of ZxZ7. Compute (3,6) (2, 4). (b) Consider (3,6) and (2, 4) as elements of R*x Z10. Compute (3,6)-(2,4). 506 CHAPTER 15 INTRODUCTION TO GROUPS (c) Consider (3,6) and (2,4) as elements of Q*x Q. Compute (3,6)-(2,4).
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