Sharply k-Transitive Permutation Groups Viewed as Galois Groups

被引：0

作者：

Gomez-Molleda, Mariangeles A. ^{[2
]}

Lario, Joan-C ^{[1
]}

机构：

[1] Univ Politecn Cataluna, Dept Matemat Aplicada 2, E-08028 Barcelona, Spain

[2] Univ Malaga, Dept Algebra Geometria & Topol, E-29071 Malaga, Spain

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2011年 / 8卷 / 04期

关键词：

Galois Group; Permutation Group; Minimal Polynomial; Class Representative; Minimal System;

D O I：

10.1007/s00009-010-0100-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The classification of finite sharply k-transitive groups was achieved by the efforts of Jordan (1873), Dickson (1905), and Zassenhaus (1936). Likewise for other families of finite groups, one expects that they are realizable as Galois groups over the field of rational numbers Q. In this article, we study some properties of the polynomials f is an element of Q[x] such that the Galois group Gal(f) acts sharply k-transitively on its roots.

引用

页码：617 / 632

页数：16

共 13 条

[1] Computing automorphisms of abelian number fields [J].

Acciaro, V ;

Klüners, J .

MATHEMATICS OF COMPUTATION, 1999, 68 (227) :1179-1186

[2]

ADAMS J, 2002, CHARACTER TABLES GL

[3] An efficient algorithm for the computation of Galois automorphisms [J].

Allombert, B .

MATHEMATICS OF COMPUTATION, 2004, 73 (245) :359-375

[4]

[Anonymous], 1992, IDEALS VARIETIES ALG, DOI DOI 10.1007/978-1-4757-2181-2

[5]

Dixon J. D., 1996, PERMUTATION GROUPS G, V163

[6] EXACT SOLUTION OF LINEAR-EQUATIONS USING P-ADIC EXPANSIONS [J].

DIXON, JD .

NUMERISCHE MATHEMATIK, 1982, 40 (01) :137-141

[7]

MCKAY J, 1997, P 1997 INT S SYMB AL, P75

[8]

PASSMAN DS, 1968, MATH LECT NOTES SERI, V17

[9]

Pilz G., 1977, Mathematics Studies, V23

[10]

Robinson D. J. S., 1996, GRAD TEXTS MATH, V80

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