‎we pursue further our‎ ‎investigation‎, ‎begun in [h.~smith‎, ‎groups with all subgroups subnormal or‎ ‎nilpotent-by-{c}hernikov‎, ‎emph{rend‎. ‎sem‎. ‎mat‎. ‎univ‎. ‎padova}‎ ‎126 (2011)‎, ‎245--253] and continued in [g.~cutolo and h.~smith‎, ‎locally finite groups with all subgroups‎ ‎subnormal or nilpotent-by-{c}hernikov‎. ‎emph{centr‎. ‎eur‎. ‎j‎. ‎math.} (to appear)] ‎‎‎of groups $g$ in w...

We establish a surprising correspondence between groups definable in o-minimal structures and linear algebraic groups, the nilpotent case. It turns out that context, like for finite nilpotency is equivalent to normalizer property or uniqueness of Sylow subgroups, provided maximal normal torsion-free subgroup nilpotent. As consequence, we show decompositions prove Lie group an expansion reals if...

One way to view Theorem 1.1 is as a statement that the algebraic structure of a finitely generated profinite group somehow also encodes the topological structure. That is, if one wishes to know the open subgroups of a profinite group G, a topological property, one must only consider the subgroups of G of finite index, an algebraic property. As profinite groups are compact topological spaces, an...

Suppose that all hyperbolic groups are residually finite. The following statements follow: In relatively hyperbolic groups with peripheral structures consisting of finitely generated nilpotent subgroups, quasiconvex subgroups are separable; Geometrically finite subgroups of non-uniform lattices in rank one symmetric spaces are separable; Kleinian groups are subgroup separable. We also show that...

A subgroup H of a finite group G is said to be W -S-permutable in G if there is a subgroup K of G such that G = HK and H ∩K is a nearly S-permutable subgroup of G. In this article, we analyse the structure of a finite group G by using the properties of W -S-permutable subgroups and obtain some new characterizations of finite p-nilpotent groups and finite supersolvable groups. Some known results...

we call $h$ an $ss$-embedded subgroup of $g$ if there exists a‎ ‎normal subgroup $t$ of $g$ such that $ht$ is subnormal in $g$ and‎ ‎$hcap tleq h_{sg}$‎, ‎where $h_{sg}$ is the maximal $s$-permutable‎ ‎subgroup of $g$ contained in $h$‎. ‎in this paper‎, ‎we investigate the‎ ‎influence of some $ss$-embedded subgroups on the structure of a‎ ‎finite group $g$‎. ‎some new results were obtained.‎

Let $X$ be a (smooth) compact complex surface. We show that the torsion subgroup of biholomorphic automorphism group $\operatorname{Aut}(X)$ is virtually nilpotent. Moreover, we study Tits alternative and virtual derived length solvable subgroups $\operatorname{Aut}(X)$.

Given a scheme in characteristic p together with a lifting modulo p2, we construct a functor from a category of suitably nilpotent modules with connection to the category of Higgs modules. We use this functor to generalize the decomposition theorem of Deligne-Illusie to the case of de Rham cohomology with coefficients.

This is a toy example to illustrate some of the techniques of fusion and transfer as described in Gorenstein’s text Finite Groups. Finite groups with a unique subgroup of order p (p an odd prime) are classified in terms of a cyclic p′-extension of relatively simple combinatorial data. This note is intended to address a slightly misstated exercise in somewhat more detail and to be a toy example ...

The group D(P ) of all endo-permutation modules for a finite p-group P is a finitely generated abelian group. We prove that its torsion-free rank is equal to the number of conjugacy classes of non-cyclic subgroups of P . We also obtain partial results on its torsion subgroup. We determine next the structure of Q⊗D(−) viewed as a functor, which turns out to be a simple functor SE,Q , indexed by ...