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1.
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
2.
Of interest are the subgroups of various groups which have nonempty intersection with each class of conjugate elements of the group under study. We call these subgroups conjugately dense and study Neumann's problem of describing them in the Chevalley groups over a field. The main theorem lists all conjugately dense subgroups of the Chevalley groups of Lie rank 1 over a locally finite field. 相似文献
3.
V. V. Bludov 《Algebra and Logic》1998,37(3):151-156
It is proved that locally nilpotent groups with the minimal condition on centralizers are hypercentral, and that the Fitting
subgroup of a group with the minimal condition on centralizers of normal subgroups is nilpotent.
Supported by RFFR grant No. 96-01-00358.
Translated fromAlgebra i Logika, Vol. 37, No. 3, pp. 270–278, May–June, 1998. 相似文献
4.
V. G. Bardakov 《Algebra and Logic》1997,36(5):288-301
We study into widths of verbal subgroups of HNN-extensions, and of groups with one defining relation. It is proved that if
a group G* is an HNN-extension and the connected subgroups in G* are distinct from a base of the extension, then every verbal subgroup V(G*) has infinite width relative to a finite proper set V of words. A similar statement is proven to hold for groups presented
by one defining relation and ≥3 generators.
to Yurii I. Merzlyakov dedicated
Supported by RFFR grant No. 93-01-01513.
Translated fromAlgebra i Logika, Vol. 36, No. 5, pp. 494–517, September–October, 1997. 相似文献
5.
E. P. Vdovin 《Algebra and Logic》2007,46(2):90-119
In the paper we work to complete the classification of Carter subgroups in finite almost simple groups. In particular, it
is proved that Carter subgroups of every finite almost simple group are conjugate. Based on our previous results, together
with those obtained by F. Dalla Volta, A. Lucchini, and M. C. Tamburini, as a consequence we derive that Carter subgroups
of every finite group are conjugate.
Supported by RFBR grant No. 05-01-00797; by the Council for Grants (under RF President) for Support of Young Russian Scientists
via projects MK-1455.2005.1 and MK-3036.2007.1; by SB RAS Young Researchers Support grant No. 29; via Integration Project
No. 2006.1.2.
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Translated from Algebra i Logika, Vol. 46, No. 2, pp. 157–216, March–April, 2007. 相似文献
6.
M. V. Neshadim 《Algebra and Logic》1996,35(5):316-318
An automorphism of an arbitrary group is called normal if all subgroups of this group are left invariant by it. Lubotski [1]
and Lue [2] showed that every normal automorphism of a noncyclic free group is inner. Here we prove that every normal automorphism
of a nontrivial free product of groups is inner as well.
Supported by RFFR grant No. 13-011-1513.
Translated fromAlgebra i Logika, Vol. 35, No. 5, pp. 562–566, September–October, 1996. 相似文献
7.
V. G. Bardakov 《Algebra and Logic》2006,45(2):75-91
For every genetic code with finitely many generators and at most one relation, a braid group is introduced. The construction
presented includes the braid group of a plane, braid groups of closed oriented surfaces, Artin— Brieskorn braid groups of
series B, and allows us to study all of these groups from a unified standpoint. We clarify how braid groups in genetic code
are structured, construct words in the normal form, look at torsion, and compute width of verbal subgroups. It is also stated
that the system of defining relations for a braid group in two-dimensional manifolds presented in a paper by Scott is inconsistent.
Supported by RFBR grant No. 02-01-01118.
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Translated from Algebra i Logika, Vol. 45, No. 2, pp. 131–158, March–April, 2006. 相似文献
8.
O. V. Bogopolskii 《Algebra and Logic》1997,36(3):155-163
It is proved that commensurable hyperbolic groups are bi-Lipschitz equivalent. Therefore, subgroups of finite index in an
arbitrary hyperbolic group also share this property. In addition, it is shown that any two separated nets Γ1 and Γ2 in the hyperbolic space Hn of dimension n≥2 are bi-Lipschitz-equivalent. These results answer the questions posed in [1].
Supported by RFFR grant No. 96-01-01781.
Translated fromAlgebra i Logika, Vol. 36, No. 3, pp. 259–272, May–June, 1997. 相似文献
9.
K. N. Ponomaryov 《Algebra and Logic》1996,35(5):319-329
A connected solvable algebraic group is called minimal if its center is trivial and it has no proper connected subgroups with
trivial center. We show that abstract isomorphisms of minimal groups defined over fields of characteristic zero are standard.
Supported by RFFR grants Nos. 96-01-01678 and 96-01-01675, and by the State Committee for Higher Education of Russia, grant
No. 2.
Translated fromAlgebra i Logika, Vol. 35, No. 5, pp. 567–586, September–October, 1996. 相似文献
10.
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
11.
We describe the structure of the lattice of normal subgroups of the group of local isometries of the boundary of a spherically
homogeneous tree LIsom ∂T. It is proved that every normal subgroup of this group contains its commutant. We characterize the quotient group of the
group LIsom ∂T by its commutant.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 10, pp. 1350–1356, October, 2008. 相似文献
12.
E. P. Vdovin 《Algebra and Logic》2000,39(5):301-312
Orders and the structure of large nilpotent subgroups in all finite simple groups are determined. In particular, it is proved
that if G is a finite simple non-Abelian group, and N is some of its nilpotent subgroups, then |N|2<|G|.
Supported through FP “Integration” project No. 274, by RFFR grant No. 99-01-00550, by International Soros Education Program
for Exact Sciences (ISEP) grant No. S99-56, and by a SO RAN grant for Young Scientists, Presidium Decree No. 83 of 03/10/2000.
Translated fromAlgebra i Logika, Vol. 39, No. 5, pp. 526–546, September—October, 2000. 相似文献
13.
14.
For partially commutative metabelian groups, annihilators of elements of commutator subgroups are described; canonical representations
of elements are defined; approximability by torsion-free nilpotent groups is proved; centralizers of elements are described.
Also, it is proved that two partially commutative metabelian groups have equal elementary theories iff their defining graphs
are isomorphic, and that every partially commutative metabelian group is embeddable in a metabelian group with decidable universal
theory.
Dedicated to V. N. Remeslennikov on the occasion of his 70th birthday
Supported by RFBR (project No. 09-01-00099).
Translated from Algebra i Logika, Vol. 48, No. 3, pp. 309–341, May–June, 2009. 相似文献
15.
A number of conditions are specified which are sufficient for totally ordered groups with polycyclic factor group to contain
a finite normal series of convex subgroups whose factors possess good enough properties. In any case studying such totally
ordered groups is reduced to treating extensions of these groups as well as their virtually o-equivalent extensions. The concept
of a virtually o-equivalent extension is a particular case of the notion of an Archimedean extension.
Supported by RFBR project No. 03-01-00320.
Translated from Algebra i Logika, Vol. 47, No. 5, pp. 529–540, September–October, 2008. 相似文献
16.
17.
Finite groups of Lie type form the greater part of known finite simple groups. An important class of subgroups of finite groups
of Lie type are so-called reductive subgroups of maximal rank. These arise naturally as Levi factors of parabolic groups and
as centralizers of semisimple elements, and also as subgroups with maximal tori. Moreover, reductive groups of maximal rank
play an important part in inductive studies of subgroup structure of finite groups of Lie type. Yet a number of vital questions
dealing in the internal structure of such subgroups are still not settled. In particular, we know which quasisimple groups
may appear as central multipliers in the semisimple part of any reductive group of maximal rank, but we do not know how normalizers
of those quasisimple groups are structured. The present paper is devoted to tackling this problem.
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. 47, No. 1, pp. 3–30, January–February, 2008. 相似文献
18.
L. L. Maksimova 《Algebra and Logic》2008,47(1):56-64
The notions of a weak interpolation property and of weak amalgamation are introduced. It is proved that in varieties with
the congruence extension property, the weak interpolation property is equivalent to the weak amalgamation property. In turn,
weak amalgamability of a variety is equivalent to amalgamability of a class of finitely generated simple algebras in this
variety.
Supported by RFBR (grant Nos. 06-01-00358 and 05-01-04003-NNIOa) and by INTAS (grant No. 04-77-7080).
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Translated from Algebra i Logika, Vol. 47, No. 1, pp. 94–107, January–February, 2008. 相似文献
19.
A non-nilpotent finite group whose proper subgroups are all nilpotent is called a Schmidt group. A subgroup A is said to be
seminormal in a group G if there exists a subgroup B such that G = AB and AB1 is a proper subgroup of G, for every proper subgroup B1 of B. Groups that contain seminormal Schmidt subgroups of even order are considered. In particular, we prove that a finite
group is solvable if all Schmidt {2, 3}-subgroups and all 5-closed {2, 5}-Schmidt subgroups of the group are seminormal; the
classification of finite groups is not used in so doing. Examples of groups are furnished which show that no one of the requirements
imposed on the groups is unnecessary.
Supported by BelFBR grant Nos. F05-341 and F06MS-017.
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Translated from Algebra i Logika, Vol. 46, No. 4, pp. 448–458, July–August, 2007. 相似文献
20.
V. M. Kopytov 《Algebra and Logic》1998,37(3):170-180
We construct an example of a fully orderable group that is not locally solvable. It is also shown that a free group is embedded
in a fully orderable group. To meet these ends, use is made of a group of invertible formal power series with zero free term
under composition.
Supported by RFFR grant No. 96-01-00088.
Translated fromAlgebra i Logika, Vol. 37, No. 3, pp. 301–319, May–June, 1998. 相似文献