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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...
Abstract: Let $S_n$ be the symmetric group on $n$ points. Deza and Frankl [M. Deza and P. Frankl, On the maximum number of permutations with given maximal or minimal distance, J. Combin. Theory Ser. A...
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...
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...
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...
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...
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...
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 ...

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