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PROBLEM 5 Let G be an abelian group, and let n € Z+. Define G × S to be G × Sn as a set, with operation defined by + (x,σ) (y, v) = (x + y²(0), σ%), . where ɛ : S„ → {±1} = Z2 is the homomorphism from Problem 1. Show that G× S is a group.

PROBLEM 5 Let G be an abelian group, and let n € Z+. Define G × S to be G × Sn as a set, with operation defined by + (x,σ) (y, v) = (x + y²(0), σ%), . where ɛ : S„ → {±1} = Z2 is the homomorphism from Problem 1. Show that G× S is a group.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.4: Cosets Of A Subgroup
Problem 24E: Find two groups of order 6 that are not isomorphic.
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PROBLEM 5 Let G be an abelian group, and let n € Z+. Define G × S to be G × Sn as a set, with operation defined by + (x,σ) (y, v) = (x + y²(0), σ%), . where ɛ : S„ → {±1} = Z2 is the homomorphism from Problem 1. Show that G× S is a group.
Transcribed Image Text:PROBLEM 5 Let G be an abelian group, and let n € Z+. Define G × S to be G × Sn as a set, with operation defined by + (x,σ) (y, v) = (x + y²(0), σ%), . where ɛ : S„ → {±1} = Z2 is the homomorphism from Problem 1. Show that G× S is a group.
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