Permutative categories of classical groups over finite fields

1978 ◽  
pp. 49-165 ◽  
Author(s):  
Zbigniew Fiedorowicz ◽  
Stewart Priddy
Keyword(s):  
Finite Fields ◽  
Classical Groups

scholarly journals A recognition algorithm for non-generic classical groups over finite fields

1999 ◽  
Vol 67 (2) ◽  
pp. 223-253 ◽  
Author(s):  
Azice C. Niemeyer ◽  
Cheryl E. Praeger
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Special Linear Group ◽  
Theoretical Background ◽  
Recognition Algorithm ◽  
Large Field ◽  
Matrix Group ◽  
Classical Groups ◽  
Original Algorithm ◽  
The Matrix

AbstractIn a previous paper the authors described an algorithm to determine whether a group of matrices over a finite field, generated by a given set of matrices, contains one of the classical groups or the special linear group. The algorithm was designed to work for all sufficiently large field sizes and dimensions of the matrix group. However, it did not apply to certain small cases. Here we present an algorithm to handle the remaining cases. The theoretical background of the algorithm presented in this paper is a substantial extension of that needed for the original algorithm.

scholarly journals Generation of classical groups over finite fields

1983 ◽  
Vol 51 ◽  
pp. 9-15 ◽  
Author(s):  
Hiroyuki Ishibashi
Keyword(s):  
Finite Fields ◽  
Classical Groups

scholarly journals Geometry of classical groups over finite fields and its applications

1997 ◽  
Vol 174 (1-3) ◽  
pp. 365-381 ◽  
Author(s):  
Zhe-xian Wan
Keyword(s):  
Finite Fields ◽  
Classical Groups

scholarly journals A theorem on power series with applications to classical groups over finite fields

2001 ◽  
Vol 64 (1) ◽  
pp. 121-129
Author(s):  
Andrew J. Spencer
Keyword(s):  
Power Series ◽  
Finite Fields ◽  
Generating Functions ◽  
General Linear ◽  
Classical Groups ◽  
Orthogonal Groups

For some of the classical groups over finite fields it is possible to express the proportion of eigenvalue-free matrices in terms of generating functions. We prove a theorem on the monotonicity of the coefficients of powers of power series and apply this to the generating functions of the general linear, symplectic and orthogonal groups. This proves a conjecture on the monotonicity of the proportions of eigenvalue-free elements in these groups.

scholarly journals Cyclic Matrices in Classical Groups over Finite Fields

2000 ◽  
Vol 234 (2) ◽  
pp. 367-418 ◽  
Author(s):  
Peter M. Neumann ◽  
Cheryl E. Praeger
Keyword(s):  
Finite Fields ◽  
Classical Groups

scholarly journals On the minimal ramification problem for ℓ-groups

2010 ◽  
Vol 146 (3) ◽  
pp. 599-606 ◽  
Author(s):  
Hershy Kisilevsky ◽  
Jack Sonn
Keyword(s):  
Galois Group ◽  
Prime Number ◽  
Finite Fields ◽  
Symmetric Groups ◽  
Wreath Products ◽  
The Other ◽  
Classical Groups ◽  
Direct Products ◽  
Cyclic Groups ◽  
Other Hand

AbstractLet ℓ be a prime number. It is not known whether every finite ℓ-group of rank n≥1 can be realized as a Galois group over ${\Bbb Q}$ with no more than n ramified primes. We prove that this can be done for the (minimal) family of finite ℓ-groups which contains all the cyclic groups of ℓ-power order and is closed under direct products, (regular) wreath products and rank-preserving homomorphic images. This family contains the Sylow ℓ-subgroups of the symmetric groups and of the classical groups over finite fields of characteristic not ℓ. On the other hand, it does not contain all finite ℓ-groups.

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