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Let G be a group and let p be a prime number such that pg =...

Let G be a group and let p be a prime number such that pg = 0 for every element g ∈ G.

a.      If G is commutative under multiplication, show that the mapping

f : G → G

f(x) = xp

is a homomorphism

b.     If G is an Abelian group under addition, show that the mapping

f : G → G

f(x) = xpis a homomorphism.

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