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Unformatted text preview: An Abelian group generated by one element is called a cyclic group . • Inﬁnite cyclic groups. • Finite cyclic group. • Theorem 7.1.3 Fundamental Theorem of Finitely Generated Abelian Groups. Let G be a ﬁnitely 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 ﬀ geom.tex; April 12, 2006; 17:59; p. 165 168 CHAPTER 7. HOMOLOGY THEORY 1. ± di ﬀ geom.tex; April 12, 2006; 17:59; p. 166...
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 Spring '10
 Wong
 Algebra, Geometry, Ring, Abelian group, Cyclic group, abelian groups, ﬁnitely generated group

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