J Austral Math Soc Ser A 47 pp53--70, 1989.

Classical Groups and Generalized Simple Groups of the Lie Type

Cheng Chon Hu

(Received 16 July 1987; revised 16 June 1988)

Abstract

In this note, for any given simple group obtained from an orthogonal or unitary group of non-zero index, by a procedure similar to the construction of Chevalley groups and twisted group, we construct a simple group which is identified with the given simple classical group. The simple groups constructed in this note can be interpreted as generalized simple groups of Lie type. Thus all simple groups of Lie type of types A_n, B_n, C_n and D_n and all generalized simple groups of Lie type constructed in this note exhaust all simple classical groups with non-zero indices.

1980 AMS Subject Classification (1985 Revision): 20H20

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Authors

Cheng Chon Hu: Department of Mathematics, Xiangtan University, Xiangtan, Hunan Province, People's Republic of China.

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Last Modified: Wed Feb 19 10:27:51 2003