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Unformatted text preview: 206 3. PRODUCTS OF GROUPS The elementary divisors of a finite abelian group can be obtained from any direct product decomposition of the group with cyclic factors, as illus trated in the previous example. If G Z a 1 Z a n , then the elementary divisors are the prime power factors of the integers a 1 ;a 2 ;:::;a n . The invariant factors can be obtained from the elementary divisors by the following algorithm, which was illustrated in the example: 1. Group together the elementary divisors belonging to each prime dividing the order of G , and arrange the list for each prime in weakly decreasing order. 2. Multiply the largest entries of each list to obtain the largest in variant factor. 3. Remove the largest entry in each list. Multiply the largest re maining entries of each nonempty list to obtain the next largest invariant factor. 4. Repeat the previous step until all the lists are exhausted....
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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, Factors

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