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On the simple groups of Suzuki and Ree
Author(s) -
Wilson Robert A.
Publication year - 2013
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pds091
Subject(s) - mathematics , mathematical proof , simple (philosophy) , type (biology) , automorphism , pure mathematics , simplicity , group of lie type , classification of finite simple groups , algebraic number , lie algebra , algebra over a field , group theory , geometry , mathematical analysis , ecology , philosophy , epistemology , biology
We develop a new and uniform approach to the three families of twisted simple groups of Lie type discovered by Suzuki and Ree, without using Lie algebras. A novel type of algebraic structure is defined, whose automorphism groups are the groups in question. This leads to elementary proofs of the group orders and simplicity, as well as much information on subgroup structure and geometry.