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This lecture is part of an online math course on group theory, focusing on three groups. The concept of free abelian groups is reviewed, showing how it extends to possibly non-abelian groups. A free abelian group is universal and generated by elements such as a, b, c. The group generated by elements in an abelian group consists of elements in the form n1a + n2b, where ni are integers. The most universal way is to take a sum of copies of the group Z. The free abelian group with a finite set of generators is a sum of copies of Z.
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