2F-modules, abelian sets of roots and 2-ranks

被引：5
|
作者：
Lawther, R. [1 ]
机构：
[1] Univ Cambridge, Ctr Math Sci, DPMMS, Cambridge CB3 0WB, England
来源：
JOURNAL OF ALGEBRA | 2007年 / 307卷 / 02期
关键词：
sporadic groups; root systems; abelian sets; 2-ranks;
D O I：
10.1016/j.jalgebra.2006.10.012
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We complete the classification of the irreducible 2F-modules for quasi-simple groups by dealing with the two open cases for sporadic groups from [R.M. Guralnick, G. Malle, Classification of 2F-modules, 1, J. Algebra 257 (2002) 348-372]. The techniques developed involve abelian sets of roots within root systems, and enable us to determine the 2-ranks of the Monster, the Baby Monster and the double cover of the latter. (c) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码：614 / 642
页数：29
相关论文
共 50 条
  • [1] 2F-modules, abelian sets of roots and 2-ranks (vol 307, pg 614, 2007)
    Lawther, R.
    JOURNAL OF ALGEBRA, 2010, 324 (12) : 3677 - 3677
  • [2] Wild sets and 2-ranks of class groups
    Conner, PE
    Perlis, R
    Szymiczek, K
    ACTA ARITHMETICA, 1997, 79 (01) : 83 - 91
  • [3] SOME 2-RANKS
    BROUWER, AE
    WILBRINK, HA
    HAEMERS, WH
    DISCRETE MATHEMATICS, 1992, 106 : 83 - 92
  • [4] Classification of 2F-modules, I
    Guralnick, RM
    Malle, G
    JOURNAL OF ALGEBRA, 2002, 257 (02) : 348 - 372
  • [5] Classification of 2F-modules, II
    Guralnick, RM
    Malle, G
    FINITE GROUPS 2003, 2005, : 117 - 183
  • [6] The 2F-modules for nearly simple groups
    Guralnick, Robert M.
    Lawther, Ross
    Malle, Gunter
    JOURNAL OF ALGEBRA, 2007, 307 (02) : 643 - 676
  • [7] On the 2-ranks of a class of unitals
    Trombetti, Rocco
    Zhou, Yue
    FINITE FIELDS AND THEIR APPLICATIONS, 2016, 40 : 90 - 109
  • [8] Switched symplectic graphs and their 2-ranks
    Abiad, Aida
    Haemers, Willem H.
    DESIGNS CODES AND CRYPTOGRAPHY, 2016, 81 (01) : 35 - 41
  • [9] Switched symplectic graphs and their 2-ranks
    Aida Abiad
    Willem H. Haemers
    Designs, Codes and Cryptography, 2016, 81 : 35 - 41
  • [10] THE 2-RANKS OF CONNECTED COMPACT LIE GROUPS
    Chen, Bang-Yen
    TAIWANESE JOURNAL OF MATHEMATICS, 2013, 17 (03): : 815 - 831
12345