| 21. | In general, a finite abelian group " G " is considered.
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| 22. | The representation theory for locally compact abelian groups is described by Pontryagin duality.
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| 23. | The new combinatorial topology formally treated topological classes as abelian groups.
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| 24. | First reformulated Keller's conjecture in terms of factorizations of abelian groups.
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| 25. | The theorem also holds more generally in locally compact abelian groups.
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| 26. | Parity forms the abelian group Z 2 due to the relation.
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| 27. | In mathematical terminology, the products of these generators define a free abelian group.
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| 28. | The conjecture has been proved for finitely generated abelian groups.
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| 29. | Modules over rings are abelian groups, but modules over semirings are only commutative monoids.
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| 30. | The real line \ mathbf { R } is a locally compact abelian group.
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