| 21. | The classical groups are important examples of non-abelian topological groups.
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| 22. | This includes kernels for homomorphisms between abelian groups as a special case.
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| 23. | In particular, it is a normal, abelian subgroup.
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| 24. | Chain complexes are easily defined in abelian categories, also.
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| 25. | These groups are our first examples of infinite non-abelian groups.
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| 26. | Non simply-connected examples are given by abelian surfaces.
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| 27. | Rank of an abelian group is analogous to the order is finite.
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| 28. | Abelian groups of rank greater than 1 are sources of interesting examples.
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| 29. | An elliptic curve is an abelian variety of dimension 1.
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| 30. | Any abelian variety is isogenous to a product of simple abelian varieties.
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