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Exercise 7.9. Let G = Q be the group of rational number with addition. Consider two rational numbers a, b. Show that (a, b) is a cyclic group. (Hint: Show it is contained in a cyclic group.) Deduce that if Q had a finite set of generators, then Q would be cyclic. (We will later see that this is not true.)

Exercise 7.9. Let G = Q be the group of rational number with addition. Consider two rational numbers a, b. Show that (a, b) is a cyclic group. (Hint: Show it is contained in a cyclic group.) Deduce that if Q had a finite set of generators, then Q would be cyclic. (We will later see that this is not true.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Exercise 7.9. Let G = Q be the group of rational number with addition. Consider two rational numbers a, b. Show that (a, b) is a cyclic group. (Hint: Show it is contained in a cyclic group.) Deduce that if Q had a finite set of generators, then Q would be cyclic. (We will later see that this is not true.)
Transcribed Image Text:Exercise 7.9. Let G = Q be the group of rational number with addition. Consider two rational numbers a, b. Show that (a, b) is a cyclic group. (Hint: Show it is contained in a cyclic group.) Deduce that if Q had a finite set of generators, then Q would be cyclic. (We will later see that this is not true.)
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