Generalizations of perfect isometries between the sets of characters of finite groups

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540021
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Osaka University (2013); Osaka Kyoiku University (2010-2012)
• Principal Investigator: UNO KATSUHIRO 大阪大学, 全学教育推進機構, 教授 (70176717)
• Co-Investigator(Renkei-kenkyūsha): WAKI Katsushi 山形大学, 理学部, 教授 (30250591) ; KUNUGI Naoko 東京理科大学, 理学部, 准教授 (50362306) ; HIDA Akihiko 埼玉大学, 教育学部, 教授 (50272274) ; NARASAKI Ryo 大阪府立大学, 工業高等専門学校, 准教授 (20567929) ; ARIKI Susumu 大阪大学, 大学院情報科学研究科, 教授 (40212641) ; MIYACHI Hyoue 大阪市立大学, 理学部, 准教授 (90362227) ; OKUYAMA Tetsuro 北海道教育大学, 教育学部, 教授 (60128733)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 有限群 / 指標 / フージョン・システム / ブロック / パーフェクト・アイソメトリ / シロー部分群 / ブルーエ予想 / 有限単純群

Outline of Final Research Achievements

We classify finite simple groups having small Sylow subgroups and determine the structure of groups appearing as Sylow subgroups of those finite simple groups. Moreover, in the case where the prime is small and a Sylow group is not abelian, we determine fusion systems over such Sylow groups.
For finite simple groups appearing in the above classification with the same Sylow subgroups and the same fusion systems over them, we construct perfect isometries between the set of irreducible characters belonging to the principal blocks of them. These isometries are those defined by Broue, namely, the ordinary perfect isometries, and not generalizations of them.

Free Research Field

群および多元環の表現論