21. Let G be an abelian group with subgroup H. Let G/H be the set ofcosets of H in G. Define multiplication of congruence classes byaH.bH = abH.Prove that if aH = a'H and bH = b'H, then abH = a'b'H, and somultiplication of cosets is well-defined. Prove that G/H is an abeliangroup with this multiplication. This is called the quotient group of Gby H.

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Answered: 21. Let G be an abelian group with…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.6: Quotient Groups

Problem 32E: 32. Let be a fixed element of the group . According to Exercise 20 of section 3.5, the mapping ...

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