Abstract Algebra: Cyclic and Abelian Groups
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All Abstract AlgebraIntegers and Modular ArithmeticFunctions and MappingsGroups and SubgroupsCyclic and Abelian GroupsHomomorphisms and IsomorphismsCosets Lagranges Theorem and Normal SubgroupsQuotient Groups and the Fundamental TheoremPermutation Groups and Cayleys TheoremClassification of Abelian GroupsRings and SubringsIntegral Domains and FieldsPolynomial Rings
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Show that a group G is abelian if for all elements a and b in G, a * b = b * a.
Are all cyclic groups Abelian? And are all Abelian groups cyclic?
Every cyclic group is Abelian. Prove it.