EXAMPLESQUESTION IFind the isomorphism type of the finite Abelian group given by:G = (X, Y, Z | X³y² = Z−³, (XYZ)² = 1, X³ Y²Z² = 1).Q13XYZ² = 1X²Y²Z² = 1X³Y²Z² = 1only use GL3 (Z) - row/column ops to "diaguralize"R₁-R₂R₂-2R₁323clean222325Gupthe relations:you can't divideby 2!110 12 22325C3--C₁R₂-3R,1000 2 00224/204224/220202R3-R₂10210 00200027/27 & 7/27I

As per the question we are given a finite Abelian group G and we have to find its isomorphism type.

Answered: Find the isomorphism type of the finite…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.8: Some Results On Finite Abelian Groups (optional)

Problem 11E: 11. Show that is a generating set for the additive abelian group if and only if

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13. Assume that are subgroups of the abelian group . Prove that if and only if is generated by

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Find the isomorphism type of the finite Abelian group given by: = (X, Y, Z | X³y² = Z¯³, (XYZ)² = 1, X³Y²Z² = 1).