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

页码：614 / 642

页数：29

共 50 条

[31] Special abelian Moufang sets of finite Morley rank in characteristic 2
Wiscons, Josh
JOURNAL OF GROUP THEORY, 2010, 13 (01) : 71 - 82
[32] Topological properties of definable sets in ordered Abelian groups of burden 2
Dolich, Alfred
Goodrick, John
MATHEMATICAL LOGIC QUARTERLY, 2023, 69 (02) : 147 - 164
[33] On central difference sets in certain non-abelian 2-groups
Gow, Rod
Quinlan, Rachel
JOURNAL OF COMBINATORIAL THEORY SERIES A, 2006, 113 (04) : 712 - 717
[34] On certain submodules ofWeyl modules for SO(2n+1, F) with char(F)=2
Cardinali, Ilaria
Pasini, Antonio
JOURNAL OF GROUP THEORY, 2014, 17 (04) : 559 - 588
[35] CHARACTERIZATION OF F+ INTERSECTION OF 2 SETS N
STOLL, M
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 57 (01) : 97 - 98
[36] A class of non-abelian 2-groups containing Menon difference sets
Meisner, DB
Piper, FC
Wild, PR
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1997, 62 (01) : 57 - 62
[37] A family of partial difference sets with denniston parameters in nonelementary Abelian 2-groups
Davis, JA
Xiang, Q
EUROPEAN JOURNAL OF COMBINATORICS, 2000, 21 (08) : 981 - 988
[38] Automorphisms and equivalence of bent functions and of difference sets in elementary Abelian 2-groups
Dempwolff, U
COMMUNICATIONS IN ALGEBRA, 2006, 34 (03) : 1077 - 1131
[39] A class of non-abelian 2-groups containing Menon difference sets
J Stat Plan Inference, 1 (57):
[40] EVERY FINITE ABELIAN GROUP IS THE GROUP OF RATIONAL POINTS OF AN ORDINARY ABELIAN VARIETY OVER F2, F3 AND F5
Marseglia, Stefano
Springer, Caleb
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2023, 151 (02) : 501 - 510

← 1 2 3 4 5 →