On characterization of simple orthogonal groups of odd dimension in the class of periodic groups

2021 ◽  
Vol 62 (1) ◽  
pp. 97-105
Author(s):  
D. V. Lytkina ◽  
V. D. Mazurov
Keyword(s):  
Orthogonal Groups ◽  
Periodic Groups

scholarly journals A characterization of orthogonal groups over GF(2)

1980 ◽  
Vol 62 (1) ◽  
pp. 39-60 ◽  
Author(s):  
Stephen D Smith
Keyword(s):  
Orthogonal Groups

scholarly journals A theorem on generation of finite orthogonal groups

1973 ◽  
Vol 16 (4) ◽  
pp. 495-506 ◽  
Author(s):  
W. J. Wong
Keyword(s):  
Finite Fields ◽  
Simple Groups ◽  
Symplectic Groups ◽  
Finite Simple Groups ◽  
Intermediate Result ◽  
Orthogonal Groups ◽  
Generators And Relations ◽  
Groups Of Lie Type

Presentation in terms of generators and relations for the classical finite simple groups of Lie type have been given by Steinberg and Curtis [2,4]. These presentations are useful in proving characterzation theorems for these groups, as in the author's work on the projective symplectic groups [5]. However, in some cases, the application is not quite instantaneous, and an intermediate result is needed to provide a presentation more suitable for the situation in hand. In this paper we prove such a result, for the orthogonal simple groups over finite fields of odd characteristic. In a subsequent article we shall use this to give a characterization of these groups in terms of the structure of the centralizer of an involution.

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