On the maximal subgroups of the finite classical groups

1984 ◽  
Vol 76 (3) ◽  
pp. 469-514 ◽  
Author(s):  
M. Aschbacher
Keyword(s):  
Maximal Subgroups ◽  
Classical Groups ◽  
Finite Classical Groups

scholarly journals Constructing Maximal Subgroups of Classical Groups

2005 ◽  
Vol 8 ◽  
pp. 46-79 ◽  
Author(s):  
Derek F. Holt ◽  
Colva M. Roney-Dougal
Keyword(s):  
Polynomial Time ◽  
Maximal Subgroups ◽  
Classical Groups ◽  
Natural Representation ◽  
Degree Polynomial ◽  
Low Degree ◽  
Finite Classical Groups

AbstractThe maximal subgroups of the finite classical groups are divided by a theorem of Aschbacher into nine classes. In this paper, the authors show how to construct those maximal subgroups of the finite classical groups of linear, symplectic or unitary type that lie in the first eight of these classes. The ninth class consists roughly of absolutely irreducible groups that are almost simple modulo scalars, other than classical groups over the same field in their natural representation. All of these constructions can be carried out in low-degree polynomial time.

On Invariants of Some Maximal Subgroups of Finite Classical Groups

2012 ◽  
Vol 19 (01) ◽  
pp. 149-158
Author(s):  
Jizhu Nan ◽  
Yufang Qin
Keyword(s):  
Polynomial Rings ◽  
Maximal Subgroups ◽  
Linear Groups ◽  
Classical Groups ◽  
Invariant Rings ◽  
Finite Classical Groups ◽  
Finite Linear

The maximal subgroups of the finite classical groups are divided into nine classes by Aschbacher's theorem. In this paper, we give explicit transcendental bases of the invariant subfields of those maximal subgroups of classical groups of linear, symplectic and unitary cases that lie in the first two of these classes. Also, we show that the invariant rings of the maximal subgroups of the finite linear groups that lie in the first class are polynomial rings.

scholarly journals Power series coefficients for probabilities in finite classical groups

2006 ◽  
Vol 305 (2) ◽  
pp. 1212-1237
Author(s):  
John R. Britnell ◽  
Jason Fulman
Keyword(s):  
Power Series ◽  
Classical Groups ◽  
Finite Classical Groups

scholarly journals The sylow 2-subgroups of the finite classical groups

1964 ◽  
Vol 1 (2) ◽  
pp. 139-151 ◽  
Author(s):  
Roger Carter ◽  
Paul Fong
Keyword(s):  
Classical Groups ◽  
Finite Classical Groups
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