scholarly journals Classification of Subgroups of Symplectic Groups Over Finite Fields Containing a Transvection

2016 ◽  
Vol 49 (2) ◽  
Author(s):  
S. Arias-de-Reyna ◽  
L. Dieulefait ◽  
G. Wiese
Keyword(s):  
Finite Fields ◽  
Symplectic Groups ◽  
Finite Subgroups

AbstractIn this note, we give a self-contained proof of the following classification (up to conjugation) of finite subgroups of GSp

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.

scholarly journals THE -GENERATION OF THE SPECIAL LINEAR GROUPS OVER FINITE FIELDS

2016 ◽  
Vol 95 (1) ◽  
pp. 48-53 ◽  
Author(s):  
MARCO ANTONIO PELLEGRINI
Keyword(s):  
Finite Fields ◽  
Simple Groups ◽  
Linear Groups ◽  
Finite Simple Groups ◽  
Special Linear ◽  
Special Linear Groups

We complete the classification of the finite special linear groups $\text{SL}_{n}(q)$ which are $(2,3)$-generated, that is, which are generated by an involution and an element of order $3$. This also gives the classification of the finite simple groups $\text{PSL}_{n}(q)$ which are $(2,3)$-generated.

A classification of algorithms for multiplying polynomials of small degree over finite fields

1992 ◽  
Vol 13 (4) ◽  
pp. 577-588 ◽  
Author(s):  
Amir Averbuch ◽  
Nader H Bshouty ◽  
Michael Kaminski
Keyword(s):  
Finite Fields ◽  
Small Degree

scholarly journals On the faithful representations, of degree 2n, of certain extensions of 2-groups by orthogonal and symplectic groups

1995 ◽  
Vol 58 (2) ◽  
pp. 232-247 ◽  
Author(s):  
S. P. Glasby
Keyword(s):  
Cyclic Group ◽  
Projective Representation ◽  
Faithful Representation ◽  
Explicit Description ◽  
Symplectic Groups ◽  
Classical Groups ◽  
Central Extensions ◽  
Central Product ◽  
Extraspecial Group

AbstractIf R is a 2-group of symplectic type with exponent 4, then R is isomorphic to the extraspecial group , or to the central product 4 o 21+2n of a cyclic group of order 4 and an extraspecial group, with central subgroups of order 2 amalgamated. This paper gives an explicit description of a projective representation of the group A of automorphisms of R centralizing Z(R), obtained from a faithful representation of R of degree 2n. The 2-cocycle associated with this projective representation takes values which are powers of −1 if R is isomorphic to and powers of otherwise. This explicit description of a projective representation is useful for computing character values or computing with central extensions of A. Such central extensions arise naturally in Aschbacher's classification of the subgroups of classical groups.

Atmospheric effect on classification of finite fields

1984 ◽  
Vol 15 (2) ◽  
pp. 95-118 ◽  
Author(s):  
Yoram J. Kaufman ◽  
Robert S. Fraser
Keyword(s):  
Finite Fields ◽  
Atmospheric Effect
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