$C_4$-Extensions of $S_n$ as Galois Groups.
نویسندگان
چکیده
منابع مشابه
Galois Groups of Maximal ̂ -extensions
Let p be an odd prime and F a field of characteristic different from p containing a primitive p\h root of unity. Assume that the Galois group G of the maximal p-extension of F has a finite normal series with abelian factor groups. Then the commutator subgroup of G is abelian. Moreover, G has a normal abelian subgroup with pro-cyclic factor group. If, in addition, F contains a primitive p2th roo...
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Writing f(T ) = (T − r1) · · · (T − rn), the splitting field of f(T ) over K is K(r1, . . . , rn). Each σ in the Galois group of f(T ) over K permutes the ri’s since σ fixes K and therefore f(r) = 0⇒ f(σ(r)) = 0. The automorphism σ is completely determined by its permutation of the ri’s since the ri’s generate the splitting field over K. A permutation of the ri’s can be viewed as a permutation ...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1995
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-12537