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1.
O. Yu. Dashkova 《Algebra and Logic》2007,46(5):297-302
We are concerned with infinite-dimensional locally soluble linear groups of infinite central dimension that are not soluble
A3-groups and all of whose proper subgroups, which are not soluble A3-groups, have finite central dimension. The structure of groups in this class is described. The case of infinite-dimensional
locally nilpotent linear groups satisfying the specified conditions is treated separately. A similar problem is solved for
infinite-dimensional locally soluble linear groups of infinite fundamental dimension that are not soluble A3-groups and all of whose proper subgroups, which are not soluble A3-groups, have finite fundamental dimension.
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Translated from Algebra i Logika, Vol. 46, No. 5, pp. 548–559, September–October, 2007. 相似文献
2.
Let B be a class of groups A which are soluble, equationally Noetherian, and have a central series A = A1 ⩾ A2 ⩾ … An ⩾ … such that ⋂An = 1 and all factors An/An+1 are torsion-free groups; D is a direct product of finitely many cyclic groups of infinite or prime orders. We prove that
the wreath product D ≀ A is an equationally Noetherian group. As a consequence we show that free soluble groups of arbitrary
derived lengths and ranks are equationally Noetherian.
Supported by RFBR grant No. 05-01-00292.
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Translated from Algebra i Logika, Vol. 46, No. 1, pp. 46–59, January–February, 2007. 相似文献
3.
O. Yu. Dashkova 《Siberian Mathematical Journal》2008,49(6):1023-1033
Under study are the solvable nonabelian linear groups of infinite central dimension and sectional p-rank, p ≥ 0, in which all proper nonabelian subgroups of infinite sectional p-rank have finite central dimension. We describe the structure of the groups of this class. 相似文献
4.
Kurt FALK Bernd O. STRATMANN 《数学学报(英文版)》2006,22(2):431-446
In this paper, we study exhaustions, referred to as p-restrictions, of arbitrary nonelementary Kleinian groups with at most finitely many bounded parabolic elements. Special emphasis is put on the geometrically infinite case, where we obtain that the limit set of each of these Kleinian groups contains an infinite family of closed subsets, referred to as p-restricted limit sets, such that there is a Poincaré series and hence an exponent of convergence δp, canonically associated with every element in this family. Generalizing concepts which are well known in the geometrically finite case, we then introduce the notion of p-restricted Patterson measure, and show that these measures are non-atomic, δp-harmonic, δp-subconformal on special sets and δp-conformal on very special sets. Furthermore, we obtain the results that each p-restriction of our Kleinian group is of δp-divergence type and that the Hausdorff dimension of the p-restricted limit set is equal to δp. 相似文献
5.
We prove that if the existence of a supercompact cardinal is consistent with ZFC, then it is consistent with ZFC that the
p-rank of Ext
ℤ(G, ℤ) is as large as possible for every prime p and for any torsion-free Abelian group G. Moreover, given an uncountable
strong limit cardinal μ of countable cofinality and a partition of Π (the set of primes) into two disjoint subsets Π0 and Π1, we show that in some model which is very close to ZFC, there is an almost free Abelian group G of size 2μ = μ+ such that the p-rank of Ext
ℤ(G, ℤ) equals 2μ = μ+ for every p ∈ Π0 and 0 otherwise, that is, for p ∈ Π1.
Number 874 in Shelah’s list of publications. Supported by the German-Israeli Foundation for Scientific Research & Development
project No. I-706-54.6/2001.
Supported by a grant from the German Research Foundation DFG.
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Translated from Algebra i Logika, Vol. 46, No. 3, pp. 369–397, May–June, 2007. 相似文献
6.
Leonid A. Kurdachenko Jose M. Muñoz-Escolano Javier Otal Nicolaj N. Semko 《Geometriae Dedicata》2009,138(1):69-81
Let F be a field and V a vector space over F. If G is a subgroup of GL(V, F), then we define the central dimension of
G (denoted by centdim
F
G) as the F-dimension of the factor-space V/C
V
(G). In this paper, we continue the study of locally nilpotent linear groups satisfying the weak minimal or the weak maximal
condition on their subgroups of infinite central dimension started in Kurdachenko et al. (Publ Mat 52:151–169, 2008).
Supported by Proyecto MTM2007-60994 of Dirección General de Investigación MEC (Spain). 相似文献
7.
O. Yu. Dashkova 《Ukrainian Mathematical Journal》2012,63(9):1379-1389
We study a
\mathbbZG \mathbb{Z}G -module A such that
\mathbbZ \mathbb{Z} is the ring of integer numbers, the group G has an infinite sectional p-rank (or an infinite 0-rank), C
G
(A) = 1, A is not a minimax
\mathbbZ \mathbb{Z} -module, and, for any proper subgroup H of infinite sectional p-rank (or infinite 0-rank, respectively), the quotient module A/C
A
(H) is a minimax
\mathbbZ \mathbb{Z} -module. It is shown that if the group G is locally soluble, then it is soluble. Some properties of soluble groups of this kind are discussed. 相似文献
8.
Two groups are said to be isospectral if they share the same set of element orders. For every finite simple linear group L
of dimension n over an arbitrary field of characteristic 2, we prove that any finite group G isospectral to L is isomorphic
to an automorphic extension of L. An explicit formula is derived for the number of isomorphism classes of finite groups that
are isospectral to L. This account is a continuation of the second author's previous paper where a similar result was established
for finite simple linear groups L in a sufficiently large dimension (n > 26), and so here we confine ourselves to groups of
dimension at most 26.
Supported by RFBR (project Nos. 08-01-00322 and 06-01-39001), by SB RAS (Integration Project No. 2006.1.2), and by the Council
for Grants (under RF President) and State Aid of Leading Scientific Schools (grant NSh-344.2008.1) and Young Doctors and Candidates
of Science (grants MD-2848.2007.1 and MK-377.2008.1).
Translated from Algebra i Logika, Vol. 47, No. 5, pp. 558–570, September–October, 2008. 相似文献
9.
E. G. Zelenyuk 《Mathematical Notes》2000,67(5):599-602
It is proved that any infinite Abelian group with finitely many elements of order two can be partitioned into two subsets
that are dense in any nondiscrete group topology, and hence contain no cosets of infinite subgroups.
Translated fromMatematicheskie Zametki, Vol. 67, No. 5, pp. 706–711, May, 2000. 相似文献
10.
Francisco J. GARCIA-PACHECO Juan B. SEOANE-SEPULVEDA 《数学学报(英文版)》2006,22(6):1805-1808
We show that there exists an infinite dimensional vector space every non-zero element of which is a non-measurable function. Moreover, this vector space can be chosen to be closed and to have dimensionβ for any cardinalityβ. Some techniques involving measure theory and density characters of Banach spaces are used. 相似文献
11.
A. V. Zavarnitsine 《Algebra and Logic》2006,45(4):220-231
We obtain the first example of an infinite series of finite simple groups that are uniquely determined by their prime graph
in the class of all finite groups. We also show that there exist almost simple groups for which the number of finite groups
with the same prime graph is equal to 2.
Supported by RFBR grant No. 05-01-00797, and by SB RAS Young Researchers Support grant No. 29 and Integration project No.
2006.1.2.
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Translated from Algebra i Logika, Vol. 45, No. 4, pp. 390–408, July–August, 2006. 相似文献
12.
N. S. Romanovskii 《Algebra and Logic》2008,47(6):426-434
A soluble group G is rigid if it contains a normal series of the form G = G1 > G2 > … > Gp > Gp+1 = 1, whose quotients Gi/Gi+1 are Abelian and are torsion-free as right ℤ[G/Gi]-modules. The concept of a rigid group appeared in studying algebraic geometry over groups that are close to free soluble.
In the class of all rigid groups, we distinguish divisible groups the elements of whose quotients Gi/Gi+1 are divisible by any elements of respective groups rings Z[G/Gi]. It is reasonable to suppose that algebraic geometry over divisible rigid groups is rather well structured. Abstract properties
of such groups are investigated. It is proved that in every divisible rigid group H that contains G as a subgroup, there is
a minimal divisible subgroup including G, which we call a divisible closure of G in H. Among divisible closures of G are divisible
completions of G that are distinguished by some natural condition. It is shown that a divisible completion is defined uniquely
up to G-isomorphism.
Supported by the Council for Grants (under RF President) and State Aid of Leading Scientific Schools (grant NSh-344.2008.1).
Translated from Algebra i Logika, Vol. 47, No. 6, pp. 762–776, November–December, 2008. 相似文献
13.
OrestD.ARTEMOVYCH 《数学学报(英文版)》2003,19(4):823-828
We characterize non-finitely generated soluble groups with the maximal condition on non-Baer subgroups and prove that a non-Baer soluble group is a ^ˇCernikov group or it has an infinite properly descending series of non-Baer subgroups. 相似文献
14.
We show that in each dimension n = 4k, k≥ 2, there exist infinite sequences of closed simply connected Riemannian n-manifolds with nonnegative sectional curvature and mutually distinct oriented cobordism type.
W. Tuschmann’s research was supported in part by a DFG Heisenberg Fellowship. 相似文献
15.
E. I. Timoshenko 《Algebra and Logic》2006,45(1):67-74
For a factor group with respect to periodic part of a group of the form F/[R′, F], an embedding in the matrix group is defined.
The criteria for a matrix to belong to an image of this group and for elements to be conjugate are specified. Some statements
having a direct bearing on groups of the form in question are proved. Application of the results obtained allows us to refine
the answer in [7] to a question by O. Chapuis concerning the universal classification of ∀-free soluble groups with two generators.
Supported by RFBR grant No. 02-01-00293 and by FP “Universities of Russia” grant No. UR.04.01.227.
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Translated from Algebra i Logika, Vol. 45, No. 1, pp. 114–125, January–February, 2006. 相似文献
16.
In Hanke and Schick (J Differ Geom 74(2):293–320, 2006) we showed non-vanishing of the universal index elements in the K-theory of the maximal C*-algebras of the fundamental groups of enlargeable spin manifolds. The underlying notion of enlargeability was the one from
Gromov and Lawson (Ann Math 111(2):209–230, 1980), involving contracting maps defined on finite covers of the given manifolds.
In the paper at hand, we weaken this assumption to the one in Gromov and Lawson (Publ IHES 58:83–196, 1983) where infinite
covers are allowed. The new idea is the construction of a geometrically given C*-algebra with trace which encodes the information given by these infinite covers. Along the way we obtain an easy proof of
a relative index theorem relevant in this context.
We thank S. Stolz and A. Thom for useful conversations regarding the research in this paper. Both authors are members of the
DFG emphasis programme “Globale Differentialgeometrie” whose support is gratefully acknowledged. 相似文献
17.
D. M. Smirnov 《Algebra and Logic》1996,35(3):204-209
A dimension of a finitely based variety V of algebras is the greatest length of a basis (that is, an independent generating
set) for the SC-theory SC(V) with the strong Mal'tsev conditions satisfied in V. A dimension is said to be infinite if the
lengths of bases in SC(V) are unbounded. We prove that the dimension of a Cantor variety Cm,n in the general form, i.e., with n>m≥1, is infinite. The algorithm of constructing a basis of any given length in SC(Cm,n) is presented. By contrast, any Post variety Pn generated by a primal algebra of order n>1 is shown to have a finite dimension not exceeding the number of maximal subalgebras
in the iterative Post algebra over the set {0,1,…,n−1}. Specifically, the dimension of the variety of Boolean algebras is
at most four.
Translated fromAlgebra i Logika, Vol. 35, No. 3, pp. 359–369, May–June, 1996. 相似文献
18.
V. V. Bludov 《Algebra and Logic》2005,44(6):370-380
We give examples of linearly ordered groups that are not embeddable in divisible orderable. In the first example, the group
does not embed in any divisible group with strictly isolated unity. In the second example, the group in question is an O*-group,
and in the third, it is a group with a central system of convex subgroups.
To my teacher A. I. Kokorin
Supported by RFBR grant Nos. 96-01-00358, 99-01-00335, and 03-01-00320.
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Translated from Algebra i Logika, Vol. 44, No. 6, pp. 664–681, November–December, 2005. 相似文献
19.
N. S. Romanovskii 《Algebra and Logic》2009,48(2):147-160
A group G is said to be rigid if it contains a normal series of the form G = G
1 > G
2 > … > G
m
> G
m + 1 = 1, whose quotients G
i
/G
i + 1 are Abelian and are torsion free as right Z[G/G
i
]-modules. In studying properties of such groups, it was shown, in particular, that the above series is defined by the group
uniquely. It is known that finitely generated rigid groups are equationally Noetherian: i.e., for any n, every system of equations in x
1, …, x
n
over a given group is equivalent to some of its finite subsystems. This fact is equivalent to the Zariski topology being
Noetherian on G
n
, which allowed the dimension theory in algebraic geometry over finitely generated rigid groups to have been constructed.
It is proved that every rigid group is equationally Noetherian.
Supported by RFBR (project No. 09-01-00099) and by the Russian Ministry of Education through the Analytical Departmental Target
Program (ADTP) “Development of Scientific Potential of the Higher School of Learning” (project No. 2.1.1.419).
Translated from Algebra i Logika, Vol. 48, No. 2, pp. 258–279, March–April, 2009. 相似文献
20.
Karin Melnick 《Geometriae Dedicata》2007,126(1):131-154
We prove results toward classifying compact Lorentz manifolds on which Heisenberg groups act isometrically. We give a general
construction, leading to a new example, of codimension-one actions – those for which the dimension of the Heisenberg group
is one less than the dimension of the manifold. The main result is a classification of codimension-one actions, under the
assumption they are real-analytic. 相似文献