7. Prove with reasons why the following are not groups (A) ★ 0 1 2 * 3 5 0 1 2 0 1 2 1 2 0 2 1 0 (C) 35 53 3 5 (B) 0 1 2 0 1 2 3 3 1 2 0 1302 203 1 0 1 2 30 213 (D) 012 0 1 2 201 1 20

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.8: Some Results On Finite Abelian Groups (optional)
Problem 1E
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Question
7. Prove with reasons why the following are not groups
(A)
★
0
1
2
3
5
0 1 2
0 1 2
1 2 0
2 1 0
(C)
35
5 3
3 5
★
0
1
2
3
★
0
1
2
(B)
0
3 1 2
1 2 3
0
1 3 0 2
2 0 3 1
0 2 1
3
(D)
0 1 2
0 1 2
201
1 2 0
Transcribed Image Text:7. Prove with reasons why the following are not groups (A) ★ 0 1 2 3 5 0 1 2 0 1 2 1 2 0 2 1 0 (C) 35 5 3 3 5 ★ 0 1 2 3 ★ 0 1 2 (B) 0 3 1 2 1 2 3 0 1 3 0 2 2 0 3 1 0 2 1 3 (D) 0 1 2 0 1 2 201 1 2 0
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