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Which one of the following is not a group? (1): (8Z,+) where 8Z = {8n | n € Z} (2): (Z8, +) where the operation is addition modulo 8 (3): (G,+) where the operation is the usual addition and G= {a+b√2 a,b ≤ Q} (4): (H,-) where the operation is the usual multiplication and H = {0,1} (5): (GL(2,Q),-) where the operation is the usual matrix multiplication

Which one of the following is not a group? (1): (8Z,+) where 8Z = {8n | n € Z} (2): (Z8, +) where the operation is addition modulo 8 (3): (G,+) where the operation is the usual addition and G= {a+b√2 a,b ≤ Q} (4): (H,-) where the operation is the usual multiplication and H = {0,1} (5): (GL(2,Q),-) where the operation is the usual matrix multiplication

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Which one of the following is not a group? (1): (8Z, +) where 8Z = {8n | n E Z} (2): (Z8, +) where the operation is addition modulo 8 (3): (G,+) where the operation is the usual addition and (H₂.) (B) (8Z,+) (Z8, +) (G,+) G = {a+b√2 a, b e Q} (4): (H,) where the operation is the usual multiplication and H = {0,1} (5): (GL(2,Q),-) where the operation is the usual matrix multiplication E (GL(2,Q),.) ☐☐
Transcribed Image Text:Which one of the following is not a group? (1): (8Z, +) where 8Z = {8n | n E Z} (2): (Z8, +) where the operation is addition modulo 8 (3): (G,+) where the operation is the usual addition and (H₂.) (B) (8Z,+) (Z8, +) (G,+) G = {a+b√2 a, b e Q} (4): (H,) where the operation is the usual multiplication and H = {0,1} (5): (GL(2,Q),-) where the operation is the usual matrix multiplication E (GL(2,Q),.) ☐☐
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