منابع مشابه
Overgroups of Elementary Symplectic Groups
Let R be a commutative ring, and let l ≥ 2; for l = 2 it is assumed additionally that R has no residue fields of two elements. The subgroups of the general linear group GL(n,R) that contain the elementary symplectic group Ep(2l, R) are described. In the case where R = K is a field, similar results were obtained earlier by Dye, King, and Shang Zhi Li. In the present paper we consider a descripti...
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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...
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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...
متن کاملCountable Primitive Groups
We give a complete characterization of countable primitive groups in several settings including linear groups, subgroups of mapping class groups, groups acting minimally on trees and convergence groups. The latter category includes as a special case Kleinian groups as well as subgroups of word hyperbolic groups. As an application we calculate the Frattini subgroup in many of these settings, oft...
متن کاملDistinguishing Primitive Permutation Groups
Let G be a permutation group acting on a set V . A partition π of V is distinguishing if the only element of G that fixes each cell of π is the identity. The distinguishing number of G is the minimum number of cells in a distinguishing partition. We prove that if G is a primitive permutation group and |V | ≥ 336, its distinguishing number is two.
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2009
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788708000785