| 31. | Every projective profinite group can be realized as an absolute Galois group of a pseudo algebraically closed field.
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| 32. | There are also Galois representations that arise from auxiliary objects and can be used to study Galois groups.
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| 33. | This induces canonical continuous actions of the absolute Galois group of " K " on the lattices.
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| 34. | However, not all Galois groups have generic polynomials, a counterexample being the cyclic group of order eight.
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| 35. | The absolute Galois group transforms these particular curves into each other, and thereby also transforms the underlying dessins.
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| 36. | The Galois group of a polynomial of degree n is S _ n or a proper subgroup of that.
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| 37. | A Picard Vessiot extension is Liouvillian if and only if the connected component of its differential Galois group is solvable.
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| 38. | In terms of Galois theory, this means that is a Galois extension of, which has a cyclic Galois group.
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| 39. | This Galois group has only two elements : \ sigma \, and the identity on \ mathbb { C }.
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| 40. | Galois cohomology makes no assumption that Galois groups are abelian groups, so that this was a non-abelian theory.
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