# Category:Abelian group theory

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Abelian groups are defined a groups where a*b=b*a a,b are part of G.
Proposition: All cyclic groups are abelian
Proof:
Let G be cyclic and generated by c. Therefore there exists an a,b in G where a=c^n, b=c^m where m,n are part of the integers. Therefore a*b = c^n * c^m =c^(n+m) = c^(m+n) = c^m * c^n = b*a therefore a*b=b*a and all cyclic groups are abelian.

## Pages in category "Abelian group theory"

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