Amalgam methods applied to the structure of the finite simple groups of characteristic 2 type
Project/Area Number 
10640033

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Algebra

Research Institution  Oita University 
Principal Investigator 
TANAKA Yasuhiko Oita University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (70244150)

CoInvestigator(Kenkyūbuntansha) 
SATO Shizuka Oita University, Faculty of Engineering, Professor, 工学部, 教授 (20040719)
OHKOHCHI Shigemi Oita University, Faculty of Engineering, Professor (70128338)

Project Period (FY) 
1998 – 2001

Project Status 
Completed (Fiscal Year 2001)

Budget Amount *help 
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2001: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2000: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1999: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1998: ¥1,000,000 (Direct Cost: ¥1,000,000)

Keywords  amalgams / solvable 2 local subgroups / characteristic 2 type / finite simple groups / revision / classification / prime graphs / rivision / solvable 2 local subgroups 
Research Abstract 
The purpose of this project is to classify the finite simple groups satisfying a certain condition (A). The actual work is stated in the following threestep procedure. 1. Classify the isomorphism classes of the amalgams (X, S, Y) of a finite 2group S and finite groups X, Y containing S as their common Sylow 2subgroup satisfying the conditions : (1) both O_2(X) and O_2(Y) are nonidentity ; (2) O_2(X, Y) is identity : (3) an additional condition may be fulfilled. 2. For a finite simple group G satisfying the condition (A), find an amalgam (X, S, Y) of subgroups S, X, Y of G satisfying the above three conditions. 3. Classify the finite simple groups G satisfying the condition (A) by judging which isomorphism class in the first step the amalgam of G found in the second step is belonging to. Basically, our result is divided into three categories. First of all, when the condition (A) is said to be 'simple groups of characteristic 2 type all of whose 2local subgroups are solvable,' we study the third step above, and get a new proof of the classification of such simple groups. Our proof is much shorter and conceptually easier than the existing one. Next, more generally, when the condition (A) is 'simple groups of characteristic 2 type,' we study the third step above, and determine the structure of quadratic module of finite simple groups. In the analysis of 2local subgroups of finite simple groups of characteristic 2 type, we often encounter modules over GF(2) having quadratic 2subgroups. So we can expect that this result will apply to the study of the third step above. Finally, when the condition (A) is 'simple groups of characteristic 2 type,' we also study the geometric structure of the prime graphs of finite simple groups. Though the importance of the connected components of only odd primes was already well known, we focus attention on its connected components containing the prime 2 and even local subgroups instead of 2local subgroups.

Report
(5 results)
Research Products
(8 results)