共查询到20条相似文献,搜索用时 15 毫秒
1.
Groups with isomorphic holomorphs are said to be holomorphically isomorphic. The following problems are treated.
- What Abelian groups have the property that their holomorphic isomorphism implies the isomorphism of the groups themselves?
- Does holomorphic isomorphism of two groups, one of which is Abelian, imply the commutativity of the other group?
2.
I. E. Grinshpon 《Journal of Mathematical Sciences》2008,154(3):284-289
Two groups are said to be almost holomorphically isomorphic if each of them is isomorphic to a normal subgroup of the holomorph
of the other group. In this paper, we study normal subgroups of holomorphs of Abelian groups and highlight some torsion-free
groups for which almost holomorphic isomorphism implies isomorphism. In addition, we consider the problem of determinateness
of a group by its holomorph.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 3, pp. 9–16, 2007. 相似文献
3.
Mixed Abelian groups with isomorphic endomorphism semigroups are studied. In particular, the question of when the isomorphism of endomorphism semigroups of Abelian groups implies the isomorphism of the groups themselves is investigated. 相似文献
4.
The notion of “near isomorphism” for torsion-free Abelian groups of finite rank is well known. In particular, this concept turned out to be of importance for classifying almost completely decomposable groups. We extend near isomorphism to classes of torsion-free Abelian groups of infinite rank which are unions of bcd–groups, this is to say unions of groups which are bounded essential extensions of completely decomposable groups. Moreover, we show that nearly isomorphic groups of this class also have nearly isomorphic endomorphism rings considered as Abelian groups. 相似文献
5.
In the paper, the isomorphism problem for completely decomposable Abelian torsion-free groups of finite rank is treated under the assumption that the groups of homomorphisms of these groups into some Abelian group are isomorphic and, moreover, the endomorphism semigroups of the groups are isomorphic. 相似文献
6.
In the paper, necessary and sufficient conditions for an Abelian group A to be isomorphic to the endomorphism group End(A) are obtained. The classes of periodic Abelian groups, divisible Abelian groups, nonreduced Abelian groups, and reduced algebraically compact Abelian groups are considered. For certain classes of Abelian groups, the isomorphism problem for a group and its endomorphism group is solved under the assumption that the endomorphism group itself has the corresponding property. 相似文献
7.
I. Kh. Bekker 《Mathematical Notes》1997,61(4):399-408
In the paper, sufficient conditions for the splittability of mixed Abelian groups with periodic automorphism groups are established.
Classes of mixed splittable Abelian groups with perfect holomorphs are distinguished.
Translated fromMaternaticheskie Zametki, Vol. 61, No. 4, pp. 483–493, April, 1997.
Translated by A. I. Shtern 相似文献
8.
I. E. Grinshpon 《Journal of Mathematical Sciences》2014,197(5):595-601
In this paper, vector groups whose holomorphs are isomorphic are studied. In connection with the studied problem, the concepts of a semi-characteristic and Γ(G)-decomposition of a group are introduced. The properties of such decompositions are described. Isomorphism conditions of holomorphically isomorphic vector groups are found. 相似文献
9.
Douglas Cenzer Rodney G. Downey Jeffrey B. Remmel Zia Uddin 《Archive for Mathematical Logic》2009,48(1):115-140
We develop a theory of LOGSPACE structures and apply it to construct a number of examples of Abelian Groups which have LOGSPACE presentations. We show that all computable torsion Abelian groups have LOGSPACE presentations and we show that the groups , and the additive group of the rationals have LOGSPACE presentations over a standard universe such as the tally representation and the binary representation of the natural numbers.
We also study the effective categoricity of such groups. For example, we give conditions are given under which two isomorphic
LOGSPACE structures will have a linear space isomorphism.
相似文献
10.
Siegmund Kosarew Paul Lupascu 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2000,70(1):265-274
In this note we identify two complex structures (one is given by algebraic geometry, the other by gauge theory) on the set
of isomorphism classes of holomorphic bundles with section on a given compact complex manifold. In the case ofline bundles, these complex spaces are shown to be isomorphic to a space of effective divisors on the manifold.
The second author was partially supported by SNF, nr. 2000-055290.98/1. 相似文献
11.
V. M. Misyakov 《Journal of Mathematical Sciences》2005,128(6):3484-3486
This paper presents necessary and sufficient conditions under which isomorphism of endomorphism rings of additive groups of arbitrary associative rings with 1 implies isomorphism of these rings. For a certain class of Abelian groups, we present a criterion which shows when isomorphism of their endomorphism rings implies isomorphism of these groups. We demonstrate necessary and sufficient conditions under which an arbitrary ring is the endomorphism ring of an Abelian group. This solves Problem 84 in L. Fuchs’ “Infinite Abelian Groups.”__________Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 1, pp. 231–234, 2003. 相似文献
12.
The problem of determination of Abelian groups (up to isomorphism) by their rings of endomorphisms in the class of completely decomposable torsion-free Abelian groups has been solved earlier. For the class of direct sums of rational groups, one can speak of determination of Abelian groups by rational representations of their endomorphism rings up to equality. In this paper, we consider this problem for the class of finite direct sums of rational groups and for some subclasses. 相似文献
13.
S. Ya. Grinshpon 《代数通讯》2013,41(9):3655-3662
We study primary Abelian groups containing proper fully invariant subgroup isomorphic to the group. The admissable sequence of the Ulm–Kaplansky invariants for primary groups is used. Using these sequences, IF-groups are described in some important classes of Abelian p-group. 相似文献
14.
An Abelian group A is called correct if for any Abelian group B isomorphisms A ≅ B′ and B ≅ A′, where A′ and B′ are subgroups of the groups A and B, respectively, imply the isomorphism A ≅ B. We say that a group A is determined by its subgroups (its proper subgroups) if for any group B the existence of a bijection between the sets of all subgroups (all proper subgroups) of groups A and B such that corresponding subgroups are isomorphic implies A ≅ B. In this paper, connections between the correctness of Abelian groups and their determinability by their subgroups (their
proper subgroups) are established. Certain criteria of determinability of direct sums of cyclic groups by their subgroups
and their proper subgroups, as well as a criterion of correctness of such groups, are obtained.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 21–36, 2003. 相似文献
15.
S. Ya. Grinshpon 《Mathematical Notes》1973,14(5):979-982
A complete answer is given to the question, does isomorphism of the endomorphism groups of primary Abelian groups imply isomorphism of the groups themselves ? It is presumed that the generalized continuum hypothesis is valid. 相似文献
16.
Clara Löh 《Geometriae Dedicata》2013,164(1):97-111
We show that Cayley graphs of finitely generated Abelian groups are rather rigid. As a consequence we obtain that two finitely generated Abelian groups admit isomorphic Cayley graphs if and only if they have the same rank and their torsion parts have the same cardinality. The proof uses only elementary arguments and is formulated in a geometric language. 相似文献
17.
Let G be a finite group. A Cayley graph over G is a simple graph whose automorphism group has a regular subgroup isomorphic to G. A Cayley graph is called a CI-graph(Cayley isomorphism) if its isomorphic images are induced by automorphisms of G. A well-known result of Babai states that a Cayley graph Γ of G is a CI-graph if and only if all regular subgroups of Aut(Γ) isomorphic to G are conjugate in Aut(Γ). A semi-Cayley graph(also called bi-Cayley graph by some authors) over G is a simple graph whose automorphism group has a semiregular subgroup isomorphic to G with two orbits(of equal size). In this paper, we introduce the concept of SCI-graph(semi-Cayley isomorphism)and prove a Babai type theorem for semi-Cayley graphs. We prove that every semi-Cayley graph of a finite group G is an SCI-graph if and only if G is cyclic of order 3. Also, we study the isomorphism problem of a special class of semi-Cayley graphs. 相似文献
18.
A. M. Sebel'din 《Algebra and Logic》1994,33(4):238-241
Some conditions for torsion-free Abelian groups to be isomorphic are found; the groups in question are decomposable into a direct product of rank 1 groups with isomorphic endomorphism semigroups.Translated fromAlgebra i Logika, Vol. 33, No. 4, pp. 422–428, July-August, 1994. 相似文献
19.
余德民 《纯粹数学与应用数学》2014,30(4):341-346
构造了一类无限维李代数,它是Virasoro-like李代数的推广.研究了这类李代数的两类自同构,这两类自同构均关于映射的合成构成自同构群,一类同构于对称群S3,另一类同构于Klein交换群.得到了这类李代数一些特殊的自同态、中心.证明了这类李代数不是半单李代数. 相似文献
20.
Xiu-Chi Quan 《Acta Appl Math》1993,31(1):87-98
In this paper, we first continue our study of group duality, and prove that the duality we established earlier is natural. Then we use this naturality to study the category of commutative, cocommutative HopfC
*-algebras, and show that the category of compact Abelian semigroups and the category of commutative, cocommutative HopfC
*-algebras with units are isomorphic. By using this result, we show that the category of commutative, cocommutative quantum groups is Abelian. This is a generalization of a result of Grothendieck about the catrgory of finite-dimensional commutative, cocommutative Hopf algebras with antipodes. 相似文献