| 21. | Let L / K be a finite field extension.
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| 22. | Now consider the finite field as an extension of.
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| 23. | In particular, the finite field has a ( constant ) generator element.
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| 24. | For finite fields the Weil group is infinite cyclic.
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| 25. | In some important cases, for example finite fields, ? is surjective.
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| 26. | Important examples are linear algebraic groups over finite fields.
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| 27. | Irreducible polynomials allow us to construct the finite fields of non prime order.
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| 28. | From the finite field you construct an elliptic curve.
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| 29. | There are efficient algorithms for testing polynomial irreducibility and factoring polynomials over finite field.
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| 30. | See also general linear group over finite fields.
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