Missouri Journal of Mathematical Sciences

Centralizers of Transitive Permutation Groups and Applications to Galois Theory

Chad Awtrey, Nakhila Mistry, and Nicole Soltz

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

Missouri J. Math. Sci., Volume 27, Issue 1 (2015), 16-32.

First available in Project Euclid: 3 December 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20B35: Subgroups of symmetric groups
Secondary: 12Y05: Computational aspects of field theory and polynomials 11R32: Galois theory 11S20: Galois theory

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


Awtrey, Chad; Mistry, Nakhila; Soltz, Nicole. Centralizers of Transitive Permutation Groups and Applications to Galois Theory. Missouri J. Math. Sci. 27 (2015), no. 1, 16--32. doi:10.35834/mjms/1449161364. https://projecteuclid.org/euclid.mjms/1449161364

Export citation