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

[41] Extensions of simple modules for SL3(2f) and SU3(2f)
Pforte, Lars
COMMUNICATIONS IN ALGEBRA, 2017, 45 (10) : 4210 - 4221
[42] Additive Properties of Product Sets in the Field F (2)(p)
Glibichuk, A. A.
MOSCOW UNIVERSITY MATHEMATICS BULLETIN, 2009, 64 (01) : 1 - 6
[43] Algebraic and F-independent sets in 2-firs
Leroy, A
Ozturk, A
COMMUNICATIONS IN ALGEBRA, 2004, 32 (05) : 1763 - 1792
[44] Negative Latin square type partial difference sets in nonelementary abelian 2-groups
Davis, JA
Xiang, Q
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2004, 70 : 125 - 141
[45] Partial difference sets and amorphic Cayley schemes in non-abelian 2-groups
Feng, Tao
He, Zhiwen
Chen, Yu Qing
JOURNAL OF COMBINATORIAL DESIGNS, 2020, 28 (04) : 273 - 293
[46] TYPE-SETS OF TORSION-FREE ABELIAN-GROUPS OF RANK-2
ITO, R
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 48 (01) : 39 - 42
[47] UPTAKE OF BACTERIOPHAGE-F2 THROUGH PLANT-ROOTS
WARD, RL
MAHLER, RJ
APPLIED AND ENVIRONMENTAL MICROBIOLOGY, 1982, 43 (05) : 1098 - 1103
[48] 2-chains and square roots of Thompson's group F
Koberda, Thomas
Lodha, Yash
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2020, 40 (09) : 2515 - 2532
[49] Size of the connected components of excursion sets of χ2, t and F fields
Bell Laboratories, Lucent Technologies, 700 Mountain Avenue, Murray Hill, NJ 07974-2070, United States
Adv Appl Probab, 3 (579-595):
[50] Maximal sets of hamilton cycles in K2p-F
Fu, H. L.
Logan, S. L.
Rodger, C. A.
DISCRETE MATHEMATICS, 2008, 308 (13) : 2822 - 2829

← 1 2 3 4 5 →