Given (Z3.+mod 3) and (Zs, mod 5). Consider their direct product Z3 X Z₁" What is the product of (2,3) and (2, 4) in Z3 X Z5"? A. (4, 12) B. (4,2) C. (1, 12) D. (1, 2) Find a subgroup of Z50 X Z18 isomorphic to Z25 x Z6- A. (2) × (3) B. (5) x (3) C. (5) x (2) D. (2) × (5) What is the identity element in the group Z3 X Zs? A. (0,0) B. (0, 1) C. (1, 1) D. (0, 2)

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 45E: 45. Let . Prove or disprove that is a group with respect to the operation of intersection. (Sec. )
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Given (Z3, +mod 3) and (Zs, mod 5). Consider their direct product Z3 X Z₁
What is the product of (2, 3) and (2, 4) in Z3 X Z5¹?
A. (4, 12)
B. (4,2)
C. (1, 12)
D. (1, 2)
Find a subgroup of Z50 X Z18 isomorphic to Z25 x Z6.
A. (2) × (3)
B. (5) X (3)
C. (5) x (2)
D. (2) × (5)
What is the identity element in the group Z3 x Z₂?
A. (0,0)
B. (0, 1)
C. (1, 1)
D. (0, 2)
Transcribed Image Text:Given (Z3, +mod 3) and (Zs, mod 5). Consider their direct product Z3 X Z₁ What is the product of (2, 3) and (2, 4) in Z3 X Z5¹? A. (4, 12) B. (4,2) C. (1, 12) D. (1, 2) Find a subgroup of Z50 X Z18 isomorphic to Z25 x Z6. A. (2) × (3) B. (5) X (3) C. (5) x (2) D. (2) × (5) What is the identity element in the group Z3 x Z₂? A. (0,0) B. (0, 1) C. (1, 1) D. (0, 2)
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