The part of the decomposition of G in Theorem 11.12 corresponding to the subgroups of prime-power order can also be written in the form ℤm1 X ℤm2 X .... X ℤmr where mi divides mi+1 lor i = 1, 2,....,r - 1. The numbers m, can be shown to be unique, and are the torsion coefficients of G.
a. Find the torsion coefficients of ℤ4 X ℤ9.
b. Find the torsion coefficients of ℤ6 X ℤ12 X ℤ20.
c. Describe an algorithm to find the torsion coefficients of a direct product of cyclic groups. Proof Synopsis
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