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- W2318964080 abstract "A finite transitive permutation group G is called a Frobenius group if every element of G other than 1 leaves at most one letter fixed, and some element of G other than 1 leaves some letter fixed. It is proved in [ 20 ] (and sketched below) that if k is a number field such that SL (2, 5) and one other nonsolvable group Ŝ 5 of order 240 are realizable as Galois groups over k, then every Frobenius group is realizable over k. It was also proved in [ 20 ] that there exists a quadratic (imaginary) field over which these two groups are realizable. In this paper we prove that they are realizable over the rationals Q , hence we Obtain THEOREM 1. Every Frobenius group is realizable as the Galois group of an extension of the rational numbers Q ." @default.
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- W2318964080 date "1980-02-01" @default.
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- W2318964080 title "SL(2,5) and Frobenius Galois Groups Over Q" @default.
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- W2318964080 doi "https://doi.org/10.4153/cjm-1980-021-4" @default.
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