Automatic realizations of Galois groups with cyclic quotient of order ${p^n}$

Ján Mináč; Andrew Schultz; John Swallow

doi:10.5802/jtnb.635

Automatic realizations of Galois groups with cyclic quotient of order

p^{n}

Ján Mináč ¹; Andrew Schultz ²; John Swallow ³

¹ Department of Mathematics Middlesex College University of Western Ontario London, Ontario N6A 5B7 CANADA
² Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, IL 61801 USA
³ Department of Mathematics Davidson College Box 7046 Davidson, North Carolina 28035-7046 USA

Journal de Théorie des Nombres de Bordeaux, Volume 20 (2008) no. 2, pp. 419-430.

Abstract
Résumé

We establish automatic realizations of Galois groups among groups $M ⋊ G$ , where $G$ is a cyclic group of order $p^{n}$ for a prime $p$ and $M$ is a quotient of the group ring $𝔽_{p} [G]$ .

Nous établissons des réalisations automatiques de groupes de Galois parmi les groupes $M ⋊ G$ où $G$ est un groupe cyclique d’ordre $p^{n}$ , $p$ premier, et $M$ un groupe quotient de l’anneau $𝔽_{p} [G]$ .

Received: 2008-04-24
Published online: 2009-02-24

MR: 2477512 | Zbl: 1180.12002

DOI: 10.5802/jtnb.635
Author's affiliations:

Ján Mináč ¹; Andrew Schultz ²; John Swallow ³

¹ Department of Mathematics Middlesex College University of Western Ontario London, Ontario N6A 5B7 CANADA
² Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, IL 61801 USA
³ Department of Mathematics Davidson College Box 7046 Davidson, North Carolina 28035-7046 USA

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     title = {Automatic realizations of {Galois} groups with cyclic quotient of order ${p^n}$},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {419--430},
     publisher = {Universit\'e Bordeaux 1},
     volume = {20},
     number = {2},
     year = {2008},
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     zbl = {1180.12002},
     language = {en},
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Ján Mináč; Andrew Schultz; John Swallow. Automatic realizations of Galois groups with cyclic quotient of order ${p^n}$. Journal de Théorie des Nombres de Bordeaux, Volume 20 (2008) no. 2, pp. 419-430. doi : 10.5802/jtnb.635. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.635/

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