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Unformatted text preview: M D N and fj C i j W 1 i N g D fj D j j W 1 j N g : n The direct product decomposition of a nite abelian group with factors cyclic groups of prime power order is called the elementary divisor decomposition. The orders of the factors are called the elementary divisors of G . Example 3.6.23. Consider the example G D Z 30 Z 50 Z 28 again. The the elementary divisor decomposition of G is: G . Z 4 Z 2 Z 2 / Z 3 . Z 25 Z 5 / Z 7 : The elementary divisors are 4;2;2;3;25;5;7 . The invariant factor deccomposition can be obtained regrouping the factors as follows: G . Z 4 Z 3 Z 25 Z 7 / . Z 2 Z 5 / Z 2 Z 4 3 25 7 Z 2 5 Z 2 Z 2100 Z 10 Z 2 :...
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra

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