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Cyclical group question: Let G be a group. We say that G is cyclic if G there is one element ge G such that G = {g" | ne Z}. (a): Show that If H is a subgroup of a cyclic group, then H is cyclic. If G = Q, consider two rational numbers a and b such that (a, b) is a cyclic group. (b): Deduce that if Q had a finite set of generators, then Q would be cyclic.

Cyclical group question: Let G be a group. We say that G is cyclic if G there is one element ge G such that G = {g" | ne Z}. (a): Show that If H is a subgroup of a cyclic group, then H is cyclic. If G = Q, consider two rational numbers a and b such that (a, b) is a cyclic group. (b): Deduce that if Q had a finite set of generators, then Q would be cyclic.

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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Cyclical group question: Let G be a group. We say that G is cyclic if G there is one element ge G such that G = {g" |ne Z}. (a): Show that If H is a subgroup of a cyclic group, then H is cyclic. If G = Q, consider two rational numbers a and b such that (a, b) is a cyclic group. (b): Deduce that if Q had a finite set of generators, then Q would be cyclic.
Transcribed Image Text:Cyclical group question: Let G be a group. We say that G is cyclic if G there is one element ge G such that G = {g" |ne Z}. (a): Show that If H is a subgroup of a cyclic group, then H is cyclic. If G = Q, consider two rational numbers a and b such that (a, b) is a cyclic group. (b): Deduce that if Q had a finite set of generators, then Q would be cyclic.
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