(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let (G, °) be a group such that the mapping f from G into G defined by f(a) = a^(-1) is a homomorphism. Show that (G, °) is abelian.

3. The attempt at a solution

f(a) = a^(-1)

f(a^(-1)) = f(a)^(-1) = (a^-1)^-1 = a

in order for a group to be abelian it needs to meet the requirement a(i)*a(j) = a(j) * a(i)

° 1 a a^-1

1 1 a a^-1

a a a^2 1

a^-1 a^-1 1 a

since each side of the diagonal are the same then (G, °) is abelian.

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# Homework Help: Abelian Groups

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