Group Theory, Beijing 1984 Proceedings of an International Symposium

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1185 Group Theory, Beijing 1984 Proceedings of an International Symposium held in Beijing, Aug. 27-Sep. 8, 1984

Edited by Tuan Hsio-Fu

Springer-Verlag Berlin Heidelberg New York Tokyo

Lecture Notes in Mathematics Edited by A. Oold and B. Eckmann

1185 Group Theory, Beijing 1984 Proceedings of an International Symposium held in Beijing, Aug. 27-Sep. 8, 1984

Edited by Tuan Hsio-Fu

Springer-Verlag Berlin Heidelberg New York Tokyo

Editor

TUAN Hsio-Fu Department of Mathematics, Peking University Beijing, The People's Republic of China

Mathematics Subject Classification (1980): 05-xx, 12F-xx, 14Kxx, 17Bxx, 20-xx ISBN 3-540-16456-1 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-16456-1 Springer-Verlag New York Heidelberg Berlin Tokyo

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.

© by Springer-Verlag Berlin Heidelberg 1986 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2146/3140-543210

PREFACE From August 27 to September 8, 1984 there was held in Peking University, Beijing an International Symposium on Group Theory. As well said by Hermann Wey1: "Symmetry is a vast subject significant in art and nature.

Whenever you have to do with a structure

endowed entity, try to determine the group of those transformations which leave all structural relations undisturbed."

This passage underlies that

the group concept is one of the most fundamental and most important in modern mathematics and its applications. branch of mathematics.

Group theory is indeed a vast

The chief topics of the Symposium were finite

groups and their connections with combinatorics, classical groups, algebraic groups and Lie groups (with emphasis on connections with algebra) . The Symposium was sponsored by our Ministry of Education.

It was

conducted by an Organization Committee consisting of seven Chinese professors of group theory: Tuan Hsio Fu (Duan Xuefu)

(Peking University), Chairman

Cao Xihua (East China Normal University), Vice Chairman Wan Zhexian (Institute of System Science, Academia Sinica), Vice Chairman Yen Zhida (Nankai University) Zhang Yuanda (Wuhan University) Zeng Kencheng (Graduate School, China University of Science and Technology) Wang Efang (Peking University) Professor Hua Loo­Keng and Professor S.S.Chern kindly gave their advice and support to the Symposium. The purpose of the Symposium was to provide a timely forum for the exchange of information and encouragement of international dialogue. For this purpose, we invited eight well­known mathematicians from abroad: John G. Thompson (University of Cambridge, U.K.) Michael Aschbacher (California Institute of Technology, U.S.A.) Charles W. Curtis