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Unformatted text preview: An Abelian group generated by one element is called a cyclic group . Innite cyclic groups. Finite cyclic group. Theorem 7.1.3 Fundamental Theorem of Finitely Generated Abelian Groups. Let G be a nitely generated Abelian group with m generators. Then G is isomorphic to the direct sum of cyclic groups, G Z Z  {z } r Z k 1 Z k p , where m = r + p. The number r is called the rank of G. Proof : di geom.tex; April 12, 2006; 17:59; p. 165 168 CHAPTER 7. HOMOLOGY THEORY 1. di geom.tex; April 12, 2006; 17:59; p. 166...
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This note was uploaded on 11/26/2011 for the course MAT 4821 taught by Professor Wong during the Spring '10 term at FSU.
 Spring '10
 Wong
 Algebra, Geometry

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