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s] Given the triple Q. +, >, and its quotients Fo.†.. > with addition † and multiplication of quotients defined by [m.n]t [p.g] = [mg + np. ng], [m.n] [p.g] = [mp, nq], [m.n). [p. q) € Fo. (a) Show that the pair (Fo, t) constitutes an Abelian group. 1

s] Given the triple Q. +, >, and its quotients Fo.†.. > with addition † and multiplication of quotients defined by [m.n]t [p.g] = [mg + np. ng], [m.n] [p.g] = [mp, nq], [m.n). [p. q) € Fo. (a) Show that the pair (Fo, t) constitutes an Abelian group. 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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s] Given the triple Q. + >, and its quotients Fo.†.•> with addition † and multiplication of quotients defined by [m.n]t [p.g] = [mg + np. ng], [m.n] • [p.g] = [mp, nq], [m.n], [p.g] € Fo. (a) Show that the pair (Fo, t) constitutes an Abelian group. 1
Transcribed Image Text:s] Given the triple Q. + >, and its quotients Fo.†.•> with addition † and multiplication of quotients defined by [m.n]t [p.g] = [mg + np. ng], [m.n] • [p.g] = [mp, nq], [m.n], [p.g] € Fo. (a) Show that the pair (Fo, t) constitutes an Abelian group. 1
Expert Solution
Step 1: Definition of Abelian group

Let G be anonempty set. A binary operation ∗ defined on G which satisfies

1) a∗b∈G     ∀a,b∈G (Closure property).

2) (a∗b)∗c=a∗(b∗c)     ∀a,b,c∈G (Associative property).

3) There exists an element e∈G such thata∗e=e∗a=a     ∀a∈G (existence of identity)

4) Every a∈G there exists b∈G such that a∗b=b∗a=e , then b is called inverse of a denoted by a−1 (existence of Inverse).

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