The maximal subgroups of the classical groups

1957 ◽  
pp. 245-378 ◽  
Author(s):  
E. B. Dynkin
Keyword(s):  
Maximal Subgroups ◽  
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.

Irreducible character restrictions to maximal subgroups of low-rank classical groups of types B and C

2019 ◽  
Vol 12 (4) ◽  
pp. 607-631
Author(s):  
Kempton Albee ◽  
Mike Barnes ◽  
Aaron Parker ◽  
Eric Roon ◽  
A. A. Schaeffer Fry
Keyword(s):  
Irreducible Character ◽  
Low Rank ◽  
Maximal Subgroups ◽  
Classical Groups
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