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2. In each case determine whether the two given groups are isomorphic. Justify your answer. a) (2Z, +) and (3Z, +). b) (R – {0},;) and (R*,;)×(Z2,O). c) (Z, +) and (Z,*) where a * b = a + b – 1.

2. In each case determine whether the two given groups are isomorphic. Justify your answer. a) (2Z, +) and (3Z, +). b) (R – {0},;) and (R*,;)×(Z2,O). c) (Z, +) and (Z,*) where a * b = a + b – 1.

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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### Problem 2: Isomorphism of Groups In each case, determine whether the two given groups are isomorphic. Justify your answer. #### a) \((2\mathbb{Z}, +)\) and \((3\mathbb{Z}, +)\). #### b) \((\mathbb{R} - \{0\}, \cdot)\) and \((\mathbb{R}^+, \cdot) \times (\mathbb{Z}_2, \oplus)\). #### c) \((\mathbb{Z}, +)\) and \((\mathbb{Z}, \ast)\) where \(a \ast b = a + b - 1\).
Transcribed Image Text:### Problem 2: Isomorphism of Groups In each case, determine whether the two given groups are isomorphic. Justify your answer. #### a) \((2\mathbb{Z}, +)\) and \((3\mathbb{Z}, +)\). #### b) \((\mathbb{R} - \{0\}, \cdot)\) and \((\mathbb{R}^+, \cdot) \times (\mathbb{Z}_2, \oplus)\). #### c) \((\mathbb{Z}, +)\) and \((\mathbb{Z}, \ast)\) where \(a \ast b = a + b - 1\).
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