query: Finite Groups as Galois Groups of Field Extensions
positive_passages.docid: 23991
positive_passages.text: Every finite group is isomorphic to some Galois group for some finite normal extension of some field.
negative_passages.docid: 142707
negative_passages.text: Intermediate fields of a finite field extension that is not separable
negative_passages.docid: 103654
negative_passages.text: A finite field extension that is not simple
negative_passages.docid: 146446
negative_passages.text: Infinite Degree Algebraic Field Extensions
negative_passages.docid: 129687
negative_passages.text: Does a Galois group being $S_3$ correspond to the extension being the splitting field of a cubic?
negative_passages.docid: 155771
negative_passages.text: Product of degree of two field extensions of prime degree
negative_passages.docid: 24168
negative_passages.text: A characterisation of quadratic extensions contained in cyclic extensions of degree 4
negative_passages.docid: 117789
negative_passages.text: Computing Galois Group of $\mathbb{Q}(\sqrt{2},\sqrt{3}):\mathbb{Q}$
negative_passages.docid: 121077
negative_passages.text: Product of all elements in finite group
negative_passages.docid: 12524
negative_passages.text: Galois group of $x^3 - 2 $ over $\mathbb Q$
negative_passages.docid: 1060
negative_passages.text: Minimal polynomial of intermediate extensions under Galois extensions.
negative_passages.docid: 80295
negative_passages.text: Field extensions and algebraic/transcendental elements
negative_passages.docid: 139499
negative_passages.text: The algebraic closure of a finite field and its Galois group
negative_passages.docid: 16643
negative_passages.text: A slick proof that a field which is finitely generated as a ring is finite
negative_passages.docid: 118610
negative_passages.text: Are all extensions of finite fields cyclic?
negative_passages.docid: 42153
negative_passages.text: Every finite abelian group is the Galois group of some finite extension of the rationals
negative_passages.docid: 133770
negative_passages.text: Subgroups of finite abelian groups.