Deal with showing the uniqueness of the prime powers appearing in the prime-power decomposition of the torsion subgroup T of a finitely generated abelian group.

Using Exercise 17, show that 

provided each r_i ≥ 1.

Data from Exercise 17

Referring to Exercise 16, show that Z_p^r [p] ≈ Z_P for any r ≥ 1 and prime p.

Transcribed Image Text:

(Zp² x Zp² X X Zpm)[p] Zpx Zp X ... x Zp m factors