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November 2015 Centralizers of Transitive Permutation Groups and Applications to Galois Theory
Chad Awtrey, Nakhila Mistry, Nicole Soltz
Missouri J. Math. Sci. 27(1): 16-32 (November 2015). DOI: 10.35834/mjms/1449161364


Let $f(x)$ be an irreducible polynomial of degree $n$ defined over a field $F$, and let $G$ be the Galois group of $f$, identified as a transitive subgroup of $S_n$. Let $K/F$ be the stem field of $f$. We show the automorphism group of $K/F$ is isomorphic to the centralizer of $G$ in $S_n$. We include two applications to computing Galois groups; one in the case $F$ is the rational numbers, the other when $F$ is the 5-adic numbers.


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Chad Awtrey. Nakhila Mistry. Nicole Soltz. "Centralizers of Transitive Permutation Groups and Applications to Galois Theory." Missouri J. Math. Sci. 27 (1) 16 - 32, November 2015.


Published: November 2015
First available in Project Euclid: 3 December 2015

zbMATH: 1332.12005
MathSciNet: MR3431112
Digital Object Identifier: 10.35834/mjms/1449161364

Primary: 20B35
Secondary: 11R32 , 11S20 , 12Y05

Keywords: $p$-adic fields , centalizers , Galois group computation , normalizers , quartic extensions

Rights: Copyright © 2015 Central Missouri State University, Department of Mathematics and Computer Science


Vol.27 • No. 1 • November 2015
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