Abelian groups, Gauss periods, and normal bases

被引：12
|
作者：
Gao, SH [1 ]
机构：
[1] Clemson Univ, Dept Math Sci, Clemson, SC 29634 USA
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2001年 / 7卷 / 01期
基金：
美国国家科学基金会;
关键词：
finite fields; finite abelian groups; Gauss periods; normal bases;
D O I：
10.1006/ffta.2000.0304
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A result on finite abelian groups is first proved and then used to solve problems in finite fields. Particularly, all finite fields that have normal bases generated by general Gauss periods are characterized and it is shown how to find normal bases of low complexity. (C) 2000 Academic Press.
引用
收藏
页码：149 / 164
页数：16
相关论文
共 50 条
  • [31] COMPUTING NORMAL INTEGRAL BASES OF ABELIAN NUMBER FIELDS
    Acciaro, Vincenzo
    Savin, Diana
    JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2018, 40 (06): : 923 - 943
  • [32] A valuation criterion for normal bases in elementary abelian extensions
    Byott, Nigel P.
    Elder, G. Griffith
    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2007, 39 : 705 - 708
  • [33] NORMAL STRUCTURE OF AUTOMORPHISM GROUPS OF ABELIAN PARA-GROUPS
    HAUSEN, J
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1972, 5 (OCT): : 409 - &
  • [34] Normal sequences over finite abelian groups
    Guan, Huanhuan
    Yuan, Pingzhi
    Zeng, Xiangneng
    JOURNAL OF COMBINATORIAL THEORY SERIES A, 2011, 118 (04) : 1519 - 1524
  • [35] On Groups whose Subnormal Abelian Subgroups are Normal
    Kurdachenko, L. A.
    Otal, J.
    Subbotin, I. Ya
    ADVANCES IN GROUP THEORY AND APPLICATIONS, 2022, 14 : 67 - 94
  • [36] GROUPS WITH 3-ABELIAN NORMAL CLOSURES
    KAPPE, LC
    MORSE, RF
    ARCHIV DER MATHEMATIK, 1988, 51 (02) : 104 - 110
  • [37] Normal minimal Cayley digraphs of abelian groups
    Meng, JX
    Ying, B
    EUROPEAN JOURNAL OF COMBINATORICS, 2000, 21 (04) : 523 - 528
  • [38] CENTRALIZERS OF ABELIAN, NORMAL SUBGROUPS OF HYPERCYCLIC GROUPS
    SCHOENWA.U
    PACIFIC JOURNAL OF MATHEMATICS, 1969, 31 (01) : 197 - +
  • [39] FINDING BASES OF UNCOUNTABLE FREE ABELIAN GROUPS IS USUALLY DIFFICULT
    Greenberg, Noam
    Turetsky, Dan
    Westrick, Linda Brown
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 370 (06) : 4483 - 4508
  • [40] Normal automorphisms of a soluble product of abelian groups
    E. I. Timoshenko
    Siberian Mathematical Journal, 2015, 56 : 191 - 198
12345