Polynomial Invariants of Certain Pseudo-Symplectic Groups Over Finite Fields of Characteristic Two

2011 ◽  
Vol 39 (7) ◽  
pp. 2498-2507 ◽  
Author(s):  
Yin Chen
Keyword(s):  
Finite Fields ◽  
Symplectic Groups ◽  
Polynomial Invariants ◽  
Characteristic Two

scholarly journals Real Representations of Finite Symplectic Groups over Fields of Characteristic Two

2018 ◽  
Vol 2020 (5) ◽  
pp. 1281-1299 ◽  
Author(s):  
C Ryan Vinroot
Keyword(s):  
Irreducible Representation ◽  
Generating Function ◽  
Prime Power ◽  
Symplectic Groups ◽  
Real Numbers ◽  
The Real ◽  
Characteristic Two ◽  
Finite Symplectic Groups

Abstract We prove that when q is a power of 2 every complex irreducible representation of $\textrm{Sp}\big (2n, \mathbb{F}_{q}\big )$ may be defined over the real numbers, that is, all Frobenius–Schur indicators are 1. We also obtain a generating function for the sum of the degrees of the unipotent characters of $\textrm{Sp}\big(2n, \mathbb{F}_{q}\big )$, or of $\textrm{SO}\big(2n+1,\mathbb{F}_{q}\big )$, for any prime power q.

Triple-Cycle Permutations Over Finite Fields of Characteristic Two

2019 ◽  
Vol 30 (02) ◽  
pp. 275-292
Author(s):  
Xianping Liu ◽  
Yuan Chen ◽  
Yunge Xu ◽  
Zhimin Sun
Keyword(s):  
Finite Fields ◽  
Characteristic Two

Triple-cycle permutations over finite fields of characteristic two are studied, and some classes of triple-cycle permutations are proposed in this paper. In addition, new triple-cycle permutations can be constructed by switching construction from known ones.

Computing Logarithms in Finite Fields of Characteristic Two

1984 ◽  
Vol 5 (2) ◽  
pp. 276-285 ◽  
Author(s):  
I. F. Blake ◽  
R. Fuji-Hara ◽  
R. C. Mullin ◽  
S. A. Vanstone
Keyword(s):  
Finite Fields ◽  
Characteristic Two

Low Complexity Normal Elements over Finite Fields of Characteristic Two

2008 ◽  
Vol 57 (7) ◽  
pp. 990-1001 ◽  
Author(s):  
Ariane M. Masuda ◽  
Lucia Moura ◽  
Daniel Panario ◽  
David Thomson
Keyword(s):  
Finite Fields ◽  
Low Complexity ◽  
Characteristic Two

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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