Let R be a ring with 1, I be a nilpotent subring of R (there exists a natural number n, such that In = 0), and I be generated by {xj |j ∈ J} as ring. Write U = 1 + I, and it is a nilpotent group with class ≤ n - 1. ...Let R be a ring with 1, I be a nilpotent subring of R (there exists a natural number n, such that In = 0), and I be generated by {xj |j ∈ J} as ring. Write U = 1 + I, and it is a nilpotent group with class ≤ n - 1. Let G be the subgroup of U which is generated by {1 + xj|j ∈ J}. The group constructed in this paper indicates that the nilpotency class of G can be less than that of U.展开更多
In this paper, we study a class of soluble Lie algebras with variety relations that the commutator of m and n is zero. The aim of the paper is to consider the relationship between the Lie algebra L with the variety re...In this paper, we study a class of soluble Lie algebras with variety relations that the commutator of m and n is zero. The aim of the paper is to consider the relationship between the Lie algebra L with the variety relations and the Lie algebra L which satisfies the permutation variety relations for the permutation ψ of {3, ··· , k}.展开更多
In this paper we consider the SchrSdinger operator -△G ＋ W on the nilpotent Lie group G where the nonnegative potential W belongs to the reverse H51der class Bq1 for some q1 ≥ D and D is the dimension at infinity o...In this paper we consider the SchrSdinger operator -△G ＋ W on the nilpotent Lie group G where the nonnegative potential W belongs to the reverse H51der class Bq1 for some q1 ≥ D and D is the dimension at infinity of G. The weighted L^p -L6q estimates for the operators W^a（-△G ＋ W）^-β and W^a△G（-△G ＋ W）^-β are obtained.展开更多
设H是有限群G的一个子群,H在G中是弱Φ-可补的,如果存在G的一个子群K,使得G=HK且H∩K≤Φ(H),其中Φ(H)是H的Frattini子群.利用p阶和p^2阶子群的弱Φ-可补性,得到如下结论:1)设G是有限群,p是|G|的满足(|G|,p-1)=1的素因数.设E是G的一个...设H是有限群G的一个子群,H在G中是弱Φ-可补的,如果存在G的一个子群K,使得G=HK且H∩K≤Φ(H),其中Φ(H)是H的Frattini子群.利用p阶和p^2阶子群的弱Φ-可补性,得到如下结论:1)设G是有限群,p是|G|的满足(|G|,p-1)=1的素因数.设E是G的一个正规子群使得G/E是p-幂零群.若E p∩G N p的每个阶为p或4循环子群均在G中弱Φ-可补,那么G是p-幂零群.2)设G有限群,p是|G|满足(|G|,p^2-1)=1的素因数.设E是G的正规子群使得G/E是p-幂零的.若E p∩G N p的每个阶为p^2的子群均在G中弱Φ-可补,则G是p-幂零的.由这些结论,得到了一系列推论,推广了已知结果.展开更多
基金supported by National Basic Research Program of China (Grant No. 2006CB805904)National Natural Science Foundation of China (Grant Nos. 10631010 and 10971054)Doctoral Foundation of Ministry of Education
文摘Let R be a ring with 1, I be a nilpotent subring of R (there exists a natural number n, such that In = 0), and I be generated by {xj |j ∈ J} as ring. Write U = 1 + I, and it is a nilpotent group with class ≤ n - 1. Let G be the subgroup of U which is generated by {1 + xj|j ∈ J}. The group constructed in this paper indicates that the nilpotency class of G can be less than that of U.
文摘In this paper, we study a class of soluble Lie algebras with variety relations that the commutator of m and n is zero. The aim of the paper is to consider the relationship between the Lie algebra L with the variety relations and the Lie algebra L which satisfies the permutation variety relations for the permutation ψ of {3, ··· , k}.
基金Supported in part by NSFC(Nos.11171353,11271085,11401597)NSF of Guangdong Province of China(No.2015A030313791)+1 种基金the Fundamental Research Funds for the Central Universitiesthe Innovative Team Project of Guangdong Province(China)(No.2014KTSCX196)
基金Supported by the National Natural Science Foundation of China （Grant Nos .10726064 10901018） and the Foundation of Theorical Research of Engineering Research Institute of University of Science and Technology Beijing.
文摘In this paper we consider the SchrSdinger operator -△G ＋ W on the nilpotent Lie group G where the nonnegative potential W belongs to the reverse H51der class Bq1 for some q1 ≥ D and D is the dimension at infinity of G. The weighted L^p -L6q estimates for the operators W^a（-△G ＋ W）^-β and W^a△G（-△G ＋ W）^-β are obtained.
基金中国博士后科学基金(No20100470136No201104027)+3 种基金"Agencija za raziskovalno dejavnost Republike Slovenije"projmladi raziskovalci"Agencija za raziskovalno dejavnost Republike Slovenije"research program P1-0285资助的项目
文摘设H是有限群G的一个子群,H在G中是弱Φ-可补的,如果存在G的一个子群K,使得G=HK且H∩K≤Φ(H),其中Φ(H)是H的Frattini子群.利用p阶和p^2阶子群的弱Φ-可补性,得到如下结论:1)设G是有限群,p是|G|的满足(|G|,p-1)=1的素因数.设E是G的一个正规子群使得G/E是p-幂零群.若E p∩G N p的每个阶为p或4循环子群均在G中弱Φ-可补,那么G是p-幂零群.2)设G有限群,p是|G|满足(|G|,p^2-1)=1的素因数.设E是G的正规子群使得G/E是p-幂零的.若E p∩G N p的每个阶为p^2的子群均在G中弱Φ-可补,则G是p-幂零的.由这些结论,得到了一系列推论,推广了已知结果.
