Overgroups of some classical linear groups with applications to linear preserver problems
نویسندگان
چکیده
منابع مشابه
Some General Techniques on Linear Preserver Problems
Several general techniques on linear preserver problems are described. The first one is based on a transfer principle in Model Theoretic Algebra that allows one to extend linear preserver results on complex matrices to matrices over other algebraically closed fields of characteristic 0. The second one concerns the use of some simple geometric technique to reduce linear preserver problems to sta...
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Linear preserver problems is an active research area in matrix and operator theory. These problems involve certain linear operators on spaces of matrices or operators. We give a general introduction to the subject in this article. In the first three sections, we discuss motivation, results, and problems. In the last three sections, we describe some techniques, outline a few proofs, and discuss ...
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Determining the subgroup structure of algebraic groups (over an algebraically closed field K of arbitrary characteristic) often requires an understanding of those instances when a group Y and a closed subgroup G both act irreducibly on some module V , which is rational for G and Y . In this paper and in Overgroups of irreducible linear groups, I (J. Algebra 181 (1996), 26–69), we give a classif...
متن کاملOvergroups of Irreducible Linear Groups, I
In work spread over several decades, Dynkin ([4, 3]), Seitz ([10, 11]), and Testerman ([16]) classified the maximal closed connected subgroups of simple algebraic groups. Their analyses for the classical group cases were based primarily on a striking result: If G is a simple algebraic group and φ : G SL V is a tensor indecomposable irreducible rational representation, then with specified except...
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For a finite group $G$, let $nse(G)={m_kmid kinpi_e(G)}$, where $m_k$ is the number of elements of order $k$ in $G$ and $pi_{e}(G)$ is the set of element orders of $G$. In this paper, we prove that $Gcong L_m(2)$ if and only if $pmid |G|$ and $nse(G)=nse(L_m(2))$, where $min {n,n+1}$ and $2^n-1=p$ is a prime number.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1994
ISSN: 0024-3795
DOI: 10.1016/0024-3795(94)90480-4