Which of the following groups are cyclic? For each cyclic group, list all the generators of the group. G1 = (Z, +) G2 = (Q, +) G3 = (Q+,.) G4 = (6Z, +) G5 = {6^n|n e Z} under multiplication G6 = {a + b√2 | a, b e Z} under addition

Which of the following groups are cyclic? For each cyclic group, list all the generators of the group. G1 = (Z, +) G2 = (Q, +) G3 = (Q+,.) G4 = (6Z, +) G5 = {6^n|n e Z} under multiplication G6 = {a + b√2 | a, b e Z} under addition

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 3E: Exercises 3. Find an isomorphism from the additive group to the multiplicative group of units...

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Question

Which of the following groups are cyclic? For each cyclic group, list all the generators of the group.

G1 = (Z, +)

G2 = (Q, +)

G3 = (Q+,.)

G4 = (6Z, +)

G5 = {6^n|n e Z} under multiplication G6 = {a + b√2 | a, b e Z} under addition

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