Sur les sous-groupes nilpotents du groupe de Cremona

Résumé. Nous décrivons les sous-groupes nilpotents non virtuellement abéliens du groupe des transformations birationnelles du plan projectif complexe: un tel groupe est d'ordre fini ou virtuellement métabélien.      

关于蕴含_3C_l可图序列的极值问题(英文)

设σ（3Cl，n）是具有下述性质的最小正偶数，每个项和至少为σ（3Cl，n）的n项可图序列。都有一个实现含有长为3，4，…，l的圈．本文确定了当7≤l≤8且n≥l以及当l=9且n≥12时响σ（3Cl，n）的值．     

Finite groups with 2-nilpotent subgroups of even index

Finite groups with 2-nilpotent subgroups of even index are described. Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 700–705, May, 1997. Translated by A. I. Shtern     

Finite groups with a seminormal Hall subgroup

Tests for π-solvability of a finite group with seminormal Hall π-subgroup are established and the nilpotency of the third commutator subgroup of any group with seminormal noncyclic Sylow subgroups is proved.     

On the local and asymptotic behavior of Brownian motion on simply connected nilpotent Lie groups

The aim of this paper is to study the local and asymptotic behavior of Brownian motion on simply connected nilpotent Lie groups. We carry over a qualitative version of the Erdös-Rényi law of large numbers for Brownian motion to simply connected step 2-nilpotent Lie groups. The method applied gives rise to a proof for qualitative results concerning the modulus of continuity of Brownian motion on simply connected step 3-resp. step 2-nilpotent Lie groups without using the Ventsel-Freidlin theory as in Baldi.     

Generalized Derivations with Skew Nilpotent Values on Lie Ideals

This article gives characterizations of generalized derivations with skew nilpotent values on noncommutative Lie ideals of a prime ring. The results simultaneously generalize the ones of Herstein, Lee and Carini et al.     

所有极大子群都为SMSN-群的有限群

若有限群G的每个2-极大子群在G中次正规,则称G为SMSN-群.本文研究了有限群G的每个真子群是SMSN-群但G本身不是SMSN-群的结构,利用局部分析的方法,获得了这类群的完整分类,推广了有限群结构理论的一些成果.     

On Lorentzian Ricci solitons on nilpotent Lie groups

The aim of this article is to exhibit the variety of different Ricci soliton structures that a nilpotent Lie group can support when one allows for the metric tensor to be Lorentzian. In stark contrast to the Riemannian case, we show that a nilpotent Lie group can support a number of non‐isometric Lorentzian Ricci soliton structures with decidedly different qualitative behaviors and that Lorentzian Ricci solitons need not be algebraic Ricci solitons. The analysis is carried out by classifying all left invariant Lorentzian metrics on the connected, simply‐connected five‐dimensional Lie group having a Lie algebra with basis vectors and and non‐trivial bracket relations and , investigating the various curvature properties of the resulting families of metrics, and classifying all Lorentzian Ricci soliton structures.     

On the theta completions for maximal subalgebras

Let L be a finite dimensional Lie algebra. Then for a maximal subalgebra M of L, a 𝜃-completion for M is a subalgebra C of L such that CM and M_L?C and C∕M_L contains no non-zero ideal of L∕M_L, properly. And a 𝜃-completion C of M is said to be a strong 𝜃-completion, if C = L or there exists a subalgebra B of L such that C be maximal in B and B is not a 𝜃-completion for M. These are analogous to the concepts of 𝜃-completion and strong 𝜃-completion of a maximal subgroup of a finite group. Now, we consider the influence of these concepts on the structure of a finite dimensional Lie algebra.