College Algebra Exam Review 196

College Algebra Exam Review 196 - 206 3. PRODUCTS OF GROUPS...

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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 non-empty 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.

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