Irreducible Almost Simple Subgroups Of Classical Algebraic Groups
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Irreducible Almost Simple Subgroups of Classical Algebraic Groups
Author: Timothy C. Burness
language: en
Publisher: American Mathematical Soc.
Release Date: 2015-06-26
Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a nontrivial -restricted irreducible tensor indecomposable rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where and is a disconnected almost simple positive-dimensional closed subgroup of acting irreducibly on . Moreover, by combining this result with earlier work, they complete the classification of the irreducible triples where is a simple algebraic group over , and is a maximal closed subgroup of positive dimension.
Irreducible Geometric Subgroups of Classical Algebraic Groups
Author: Timothy C. Burness,
language: en
Publisher: American Mathematical Soc.
Release Date: 2016-01-25
Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a non-trivial irreducible tensor-indecomposable -restricted rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where is a disconnected maximal positive-dimensional closed subgroup of preserving a natural geometric structure on .
The Local Structure Theorem for Finite Groups With a Large $p$-Subgroup
Author: U. Meierfrankenfeld
language: en
Publisher: American Mathematical Soc.
Release Date: 2016-06-21
Let p be a prime, G a finite Kp-group S a Sylow p-subgroup of G and Q a large subgroup of G in S (i.e., CG(Q)≤Q and NG(U)≤NG(Q) for 1≠U≤CG(Q)). Let L be any subgroup of G with S≤L, Op(L)≠1 and Q⋬L. In this paper the authors determine the action of L on the largest elementary abelian normal p-reduced p-subgroup YL of L.