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Sieve methods in group theory I: Powers in Linear groups
Sieve Property-T Powers Linear groups Finite groups of Lie type
2011/9/14
Abstract: A general sieve method for groups is formulated. It enables one to "measure" subsets of a finitely generated group. As an application we show that if $\Gamma$ is a finitely generated non vir...
Linear groups over a locally linear division ring
Division ring algebraic strongly algebraic locally linear linear groups
2011/2/28
In this paper, in the first we give definitions of some classes of division rings which strictly contain the class of centrally finite division rings. One of our main purpose is to construct non-trivi...
Homotopy invariance for homology of linear groups: reductions and the rank two case
linear groups the rank two case
2010/11/24
We discuss the problem of homotopy invariance for homology of linear groups. Some reductions we are able to make show that homotopy invariance for linear groups follows from contractibility of a cert...
Simple Modules of Classical Linear Groups with Normal Closures of Maximal Torus Orbits
Toric variety normality simple module classical root system
2010/12/10
Let T be a maximal torus in a classical linear group G. In this paper we find all simple rational G-modules V such that for each vector v ∈ V the closure of its T -orbit is
a normal affine variety. F...
A problem of Kollar and Larsen on finite linear groups and crepant resolutions
Age deviation finite linear groups complex reflection groups
2010/12/6
The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calab...
正> The problem of determining the automorphisms of the linear groupsand the possible isomerphisms between them was first studied by O,Schreier and v.d.Waerden[1].They determined the automerphisms ofth...
Hartley´s Theorem on Representations of the General Linear Groups and Classical Groups
subgroups of classical groups representation theory of algebraic groups
2010/2/26
We suggest a new proof of Hartley's theorem on representations of the general linear groups GLn(K) where K is a field. Let H be a subgroup of GLn(K) and E the natural GLn(K)-module. Suppose that the r...
Conjugacy classes in maximal parabolic subgroups of general linear groups
Conjugacy classes parabolic subgroups linear groups
2010/10/29
We compute conjugacy classes in maximal parabolic subgroups of the general linear group. This computation proceeds by reducing to a ``matrix problem''. Such problems involve finding normal forms for ...