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40. Let G = Z6 x Z6, and let H=< (2, 2) >= {(0,0), (2, 2), (4,4)}. By Lagrange's Theorem, |G/H| = 36/3= 12, and by corollary 55, we know G/H is abelian. We will not do so in this course, but it is possible to show there are exactly two (non-isomorphic) abelian groups with 12 elements - Z12 and Zs x Z2. Assuming this is true, to which of those groups is G/H isomorphic?

40. Let G = Z6 x Z6, and let H=< (2, 2) >= {(0,0), (2, 2), (4,4)}. By Lagrange's Theorem, |G/H| = 36/3= 12, and by corollary 55, we know G/H is abelian. We will not do so in this course, but it is possible to show there are exactly two (non-isomorphic) abelian groups with 12 elements - Z12 and Zs x Z2. Assuming this is true, to which of those groups is G/H isomorphic?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 32EQ
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40. Let G = Z6 x Zs, and let H=< (2, 2) >= {(0,0), (2, 2), (4,4)}. By Lagrange's Theorem, |G/H| = 36/3= 12, and by corollary 55, we know G/H is abelian. We will not do so in this course, but it is possible to show there are exactly two (non-isomorphic) abelian groups with 12 elements - Z12 and Zs x Z2. Assuming this is true, to which of those groups is G/H isomorphic?
Transcribed Image Text:40. Let G = Z6 x Zs, and let H=< (2, 2) >= {(0,0), (2, 2), (4,4)}. By Lagrange's Theorem, |G/H| = 36/3= 12, and by corollary 55, we know G/H is abelian. We will not do so in this course, but it is possible to show there are exactly two (non-isomorphic) abelian groups with 12 elements - Z12 and Zs x Z2. Assuming this is true, to which of those groups is G/H isomorphic?
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