SATURATED FUSION SYSTEMS OVER 2-GROUPS

被引：24

作者：

Oliver, Bob ^{[1
]}

Ventura, Joana ^{[2
]}

机构：

[1] Inst Galilee, Lab Anal Geometrie & Applicat, F-93430 Villetaneuse, France

[2] Univ Tecn Lisboa, Dept Matemat, Inst Super Tecn, P-1049001 Lisbon, Portugal

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 361卷 / 12期

关键词：

Finite groups; 2-groups; fusion; simple groups; LOCAL FINITE-GROUPS; EVEN ORDER;

D O I：

10.1090/S0002-9947-09-04881-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We develop methods for listing, for a given 2-group S, all nonconstrained centerfree saturated fusion systems over S. These are the saturated fusion systems which could, potentially, include minimal examples of exotic fusion systems: fusion systems not arising from any finite group. To test our methods, we carry out this program over four concrete examples: two of order 2(7) and two of order 2(10). Our long term goal is to make a wider, more systematic search for exotic fusion systems over 2-groups of small order.

引用

页码：6661 / 6728

页数：68

共 26 条

[1]

[Anonymous], 1975, Classics in Mathematics

[2] THE ORDERS OF THE LINEAR GROUPS [J].

ARTIN, E .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1955, 8 (03) :355-366

[3]

Aschbacher M., 1986, Finite Group Theory

[4]

Aschbacher M., 1994, SPORADIC GROUPS

[5] TRANSITIVE GROUP OF EVEN ORDER, WHEREIN EACH INVOLUTION FIXES EXACTLY ONE POINT [J].

BENDER, H .

JOURNAL OF ALGEBRA, 1971, 17 (04) :527-&

[6]

Benson D., 1998, LONDON MATH SOC LECT, V252, P10

[7] ON FINITE GROUPS OF EVEN ORDER WHOSE 2-SYLOW GROUP IS A QUATERNION GROUP [J].

BRAUER, R ;

SUZUKI, M .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1959, 45 (12) :1757-1759

[8] Extensions of p-local finite groups [J].

Broto, C. ;

Castellana, N. ;

Grodal, J. ;

Levi, R. ;

Oliver, B. .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 359 (08) :3791-3858

[9] Subgroup families controlling p-local finite groups [J].

Broto, C ;

Castellana, N ;

Grodal, J ;

Levi, R ;

Oliver, B .

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2005, 91 :325-354

[10] The homotopy theory of fusion systems [J].

Broto, C ;

Levi, R ;

Oliver, B .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 16 (04) :779-856

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