共查询到20条相似文献,搜索用时 15 毫秒
1.
Risto Atanasov 《代数通讯》2013,41(6):2130-2139
A subgroup H of a group G is a solitary subgroup of G if G does not contain another isomorphic copy of H. Combining together the concepts of solitary subgroups and solvable groups, we define (normal) solitary solvable groups and (normal) strongly solitary solvable groups. We derive several results that hold for these groups and we discuss classes of groups that, under certain hypotheses, are (normal) solitary solvable and (normal) strongly solitary solvable. We also derive several results about p-groups that are solitary solvable. 相似文献
2.
Interval systems of max-separable linear equations 总被引:1,自引:0,他引:1
Katarí na Cechl rov R. A. Cuninghame-Green 《Linear algebra and its applications》2002,340(1-3):215-224
An interval system of equations is weakly solvable if at least one of its subsystems is solvable, and it is strongly solvable if all its subsystems are solvable. We give necessary and sufficient conditions enabling efficient testing of weak and strong solvability over max-plus and max-min algebras. 相似文献
3.
4.
Classical r-Matrices and Novikov Algebras 总被引:1,自引:0,他引:1
Dietrich Burde 《Geometriae Dedicata》2006,122(1):145-157
We study the existence problem for Novikov algebra structures on finite-dimensional Lie algebras. We show that a Lie algebra
admitting a Novikov algebra is necessarily solvable. Conversely we present a 2-step solvable Lie algebra without any Novikov
structure. We use extensions and classical r-matrices to construct Novikov structures on certain classes of solvable Lie algebras. 相似文献
5.
6.
Thompson’s theorem indicates that a finite group with a nilpotent maximal subgroup of odd order is solvable. As an important
application of Thompson’s theorem, a finite group is solvable if it has an abelian maximal subgroup. In this paper, we give
some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable. 相似文献
7.
The notion of PI-representable groups is introduced; these are subgroups of invertible elements of a PI-algebra over a field. It is shown that a PI-representable group has a largest locally solvable normal subgroup, and this subgroup coincides with the prime radical of the group. The prime radical of a finitely generated PI-representable group is solvable. The class of PI-representable groups is a generalization of the class of linear groups because in the groups of the former class the largest locally solvable normal subgroup can be not solvable. 相似文献
8.
N. I. Sandu 《Mathematical Notes》1978,23(4):285-287
We generalize Fischer's well-known theorem which asserts that the right associated group of a finite distributive quasigroup is solvable. We prove that the associated group of a finitely generated distributive quasigroup is solvable and that the associated group of any distributive quasigroup is locally solvable.Translated from Matematicheskie Zametki, Vol. 23, No. 4, pp. 521–526, April, 1978. 相似文献
9.
关于具有限秩的可解群 总被引:4,自引:0,他引:4
关于具有限秩的可解群本文得到了它的正规列的交换商因子的一种排序,推出了这类群的所有拟循环了群构成它的一个特征子群,了秩n的可解群的Hirsch不变量≤n,并由此界定了秩n的无挠可解群的导出长度。 相似文献
10.
Valeriy G. Bardakov 《代数通讯》2013,41(11):4809-4824
We investigate the palindromic width of finitely generated solvable groups. We prove that every finitely generated 3-step solvable group has finite palindromic width. More generally, we show the finiteness of the palindromic width for finitely generated abelian-by-nilpotent-by-nilpotent groups. For arbitrary solvable groups of step ≥3, we prove that if G is a finitely generated solvable group that is an extension of an abelian group by a group satisfying the maximal condition for normal subgroups, then the palindromic width of G is finite. We also prove that the palindromic width of ??? with respect to the set of standard generators is 3. 相似文献
11.
Michael Wüstner 《manuscripta mathematica》1996,91(1):179-194
Summary The article investigate the structure of real solvable connected Lie groups. It is described how one can decompose a solvable
Lie group in direct and semidirect products of closed connected subgroups. In particular, the commutator group, Cartan subgroups,
the center, maximal compactly embedded subgroups and tori are considered. Furthermore, one can find special solvable Lie groups
and their product decompositions, namely compactly generated solvable Lie groups and those Lie groups which are generated
by maximal compactly embedded subgroups.
This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag. 相似文献
12.
In this paper, we will discuss the properties of solvable complete Lie algebra, describe the structures of the root spaces of solvable complete Lie algebra, prove that solvable Lie algebras of maximal rank are com-plete, and construct some new complete Lie algebras from Kac-Moody algebras. 相似文献
13.
ZHU Linsheng Department of Mathematics Changshu Institute of Technology Changshu China 《中国科学A辑(英文版)》2006,49(4):477-493
A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular, the solvable quadratic Lie algebras whose Cartan subalgebras consist of semi-simple elements, the author presents a procedure to construct a class of quadratic Lie algebras from the point of view of cohomology and shows that all solvable quadratic Lie algebras can be obtained in this way. 相似文献
14.
设x是简单无向图,G是Aut(X)的一个于群,X称为G-对称的,如果G在x的1-孤(即两相邻顶点构成的有序偶)集合上的作用是传递的;x称为对称图,如果X是Aut(x)-对称的;x称为可解对称的,如果Aut(X)包含可解子群G,使X是G-对称的.本文给出了具有6P个顶点的可解对称图的一个分类,这里p≥5是素数. 相似文献
15.
Jeanne Erdman Snow 《manuscripta mathematica》1990,66(1):397-412
In this paper, invariant complex structures on four-dimensional, solvable, simply-connected real Lie groups are classified
where the dimension of the commutator is less than three. The resulting complex surfaces corresponding to these structures
are also determined. The classification problem is reduced to determining certain complex “structure” subalgebras of the complexifications
of the four-dimensional, solvable real Lie algebras. Most of the eleven types of non-abelian solvable real Lie algebras do
have complex structure subalgebras; three do not. Only three types of algebras have solvable complex structure subalgebras,
and only one possesses both abelian and solvable complex structure subalgebras. Each of the possible homogeneous surfaces
is represented in the list of resulting manifolds. 相似文献
16.
Keith A. Kearnes Emil W. Kiss Matthew A. Valeriote 《Transactions of the American Mathematical Society》1998,350(1):1-41
The aim of this paper is twofold. First some machinery is established to reveal the structure of abelian congruences. Then we describe all minimal, locally finite, locally solvable varieties. For locally solvable varieties, this solves problems 9 and 10 of Hobby and McKenzie. We generalize part of this result by proving that all locally finite varieties generated by nilpotent algebras that have a trivial locally strongly solvable subvariety are congruence permutable.
17.
A solvable cover of a graph is a regular cover whose covering transformation group is solvable. In this paper, we show that a solvable cover of a graph can be decomposed into layers of abelian covers, and also, a lift of a given automorphism of the base graph of a solvable cover can be decomposed into layers of lifts of the automorphism in the layers of the abelian covers. This procedure is applied to classify metacyclic covers of the tetrahedron branched at face-centers. 相似文献
18.
Kıvanç Ersoy 《Archiv der Mathematik》2016,106(5):401-407
In this paper, we prove that a finite group with a splitting automorphism of odd order is solvable. By using this result, we prove that a locally finite group with a splitting automorphism of odd order is locally solvable. 相似文献
19.
Xiangdong Xie 《Mathematische Annalen》2012,353(3):727-746
We describe all the self quasisymmetric maps on the ideal boundary of a particular negatively curved solvable Lie group. As applications, we derive some rigidity properties for quasiisometries of the solvable Lie group. 相似文献
20.
利用SL(2,C)中可解子群的结构,给出了SL(2k,C)中两类特殊的具有两个生成元的可解子群的结构定理.由单值群的可解性与Fuchs系统可积性之间的关系,研究对应的单值群是可解的环面上只有一个正则奇点的2k阶Fuchs方程的解Riemann曲面结构,进而研究其解的大范围性质. 相似文献