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: (a) Let p be a prime, and let G be a finite Abelian group. Show...

: (a) Let p be a prime, and let G be a finite Abelian group. Show that Gp = {x ∈ G | |x| is a power of p} is a subgroup of G. (For the identity, remember that 1 = p 0 is a power of p.) (b) Let p1, . . . , pn be pair-wise distinct primes, and let G be an Abelian group. Show that Gp1 , . . . , Gpn form direct sum in G.

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