We construct all possible noncommutative deformations of a Kleinian singularity C 2/Γ of type Dn in terms of generators and relations, and solve the problem of when two deformations are isomorphic. We prove that all isomorphisms arise naturally from the action of the normalizer NSL(2)(Γ) on C/Γ. We deduce that the moduli space of isomorphism classes of noncommutative deformations in type Dn is ...

Let Out(Fn) denote the outer automorphism group of the free group Fn with n > 3. We prove that for any finite index subgroup Γ < Out(Fn), the group Aut(Γ) is isomorphic to the normalizer of Γ in Out(Fn). We prove that Γ is co-Hopfian : every injective homomorphism Γ → Γ is surjective. Finally, we prove that the abstract commensurator Comm(Out(Fn)) is isomorphic to Out(Fn).

In this paper, we show that for every abelian subgroup H of a Garside group, some conjugate gHg consists of ultra summit elements and the centralizer of H is a finite index subgroup of the normalizer of H. Combining with the results on translation numbers in Garside groups, we obtain an easy proof of the algebraic flat torus theorem for Garside groups and solve several algorithmic problems conc...

We construct an example of a torsion free freely indecomposable finitely presented nonquasiconvex subgroup H of a word hyperbolic group G such that the limit set of G is not the limit set of a quasiconvex subgroup of G. In particular, this gives a counterexample to the conjecture of G.Swarup that a finitely presented one-ended subgroup of a word hyperbolic group is quasiconvex if and only if it...

In this paper we study the normalizer decomposition of a compact Lie group G using information fusion system F on maximal discrete p-toral subgroup. We prove that there is an injective map from set conjugacy classes chains F-centric, F-radical subgroups to p-centric, p-stubborn continuous subgroups. The bijection when π0(G) finite p-group. also classifying space chain mod p equivalent correspon...

In this paper, we introduce the notation of soft bornological group to solve problem boundedness for group. We combine set theory with bornology space produce a new structure which is called So that both product and inverse maps are bounded. As well as, study actions on sets. The aim partition into orbital classes by acting set. addition, explain centralizer, normalizer, stabilizer in details. ...

We develop the local-global theory of blocks for profinite groups. Given a field k characteristic p and group G, one may express completed algebra k[[G]] as product ∏i∈IBi closed indecomposable algebras, called G. To each block B G we associate pro-p subgroup defect B, unique up to conjugacy in give several characterizations analogy with groups finite Our main theorem is version Brauer's first ...

This paper presents the automatic extension to other languages of TERSEO, a knowledge-based system for the recognition and normalization of temporal expressions originally developed for Spanish1. TERSEO was first extended to English through the automatic translation of the temporal expressions. Then, an improved porting process was applied to Italian, where the automatic translation of the temp...