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SL(2,5) and Frobenius Galois Groups Over Q

Published online by Cambridge University Press:  20 November 2018

Jack Sonn
Jack Sonn*
Affiliation:
Technion, Israeli Institute of Technology, Haifa, Israel
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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 Ŝ5 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 numbersQ.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 2 , February 1980 , pp. 281 - 293
Copyright
Copyright © Canadian Mathematical Society 1980

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