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1.
V. V. Rimatskii 《Algebra and Logic》1999,38(4):237-247
It is proved that every finitely approximable and residually finite modal logic of depth 2 over K4 has a finite basis of admissible
inference rules. This, in particular, implies that every finitely approximable residually finite modal logic of depth at most
2 is finitely based w.r.t. admissibility. (Among logics in a larger depth or width, there are logics which do not have a finite,
or even independent, basis of admissible rules of inference.)
Translated fromAlgebra i Logika, Vol. 38, No. 4, pp. 436–455, July–August 1999. 相似文献
2.
O. V. Belegradek 《Algebra and Logic》2000,39(4):252-258
For any constructive commutative ring k with unity, we furnish an example of a residually finite, finitely generated, recursively
defined associative k-algebra with unity whose word problem is undecidable. This answers a question of Bokut’ in [3].
Translated fromAlgebra i Logika, Vol. 39, No. 4, pp. 441–451, July–August, 2000. 相似文献
3.
We present two methods of constructing amenable (in the sense of Greenleaf) actions of nonamenable groups. In the first part
of the paper, we construct a class of faithful transitive amenable actions of the free group using Schreier graphs. In the
second part, we show that every finitely generated residually finite group can be embedded into a bigger residually finite
group, which acts level-transitively on a locally finite rooted tree, so that the induced action on the boundary of the tree
is amenable on every orbit. Bibliography: 25 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 85–96. 相似文献
4.
D. N. Azarov 《Mathematical Notes》2017,101(3-4):385-390
Following A. I.Mal’tsev, we say that a group G has finite general rank if there is a positive integer r such that every finite set of elements of G is contained in some r-generated subgroup. Several known theorems concerning finitely generated residually finite groups are generalized here to the case of residually finite groups of finite general rank. For example, it is proved that the families of all finite homomorphic images of a residually finite group of finite general rank and of the quotient of the group by a nonidentity normal subgroup are different. Special cases of this result are a similar result of Moldavanskii on finitely generated residually finite groups and the following assertion: every residually finite group of finite general rank is Hopfian. This assertion generalizes a similarMal’tsev result on the Hopf property of every finitely generated residually finite group. 相似文献
5.
Non-nilpotent, finitely generated, associative nil-algebras are studied as well as their adjoint groups and Golod groups.
Solutions are given to some problems in residually finite group theory, questions posed in the Kourovka Notebook included.
Supported by RFBR grant No. 03-01-00356.
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Translated from Algebra i Logika, Vol. 45, No. 2, pp. 231–238, March–April, 2006. 相似文献
6.
Benjamin Fine Anthony M Gaglione Alexei Myasnikov Gerhard Rosenberger Dennis Spellman 《Journal of Algebra》1998,200(2):657
A groupGisfully residually freeprovided to every finite setS ⊂ G\{1} of non-trivial elements ofGthere is a free groupFSand an epimorphismhS:G → FSsuch thathS(g) ≠ 1 for allg ∈ S. Ifnis a positive integer, then a groupGisn-freeprovided every subgroup ofGgenerated bynor fewer distinct elements is free. Our main result shows that a fully residually free group of rank at most 3 is either abelian, free, or a free rank one extension of centralizers of a rank two free group. To prove this we prove that every 2-free, fully residually free group is actually 3-free. There are fully residually free groups which are not 2-free and there are 3-free, fully residually free groups which are not 4-free. 相似文献
7.
V. V. Rimatskii 《Algebra and Logic》2009,48(3):228-236
A recursive basis of inference rules is described which are instantaneously admissible in all table (residually finite) logics
extending one of the logics Int and Grz. A rather simple semantic criterion is derived to determine whether a given inference rule is admissible in all table superintuitionistic
logics, and the relationship is established between admissibility of a rule in all table (residually finite) superintuitionistic
logics and its truth values in Int.
Translated from Algebra i Logika, Vol. 48, No. 3, pp. 400–414, May–June, 2009. 相似文献
8.
Thomas S. Weigel 《代数通讯》2013,41(5):1395-1425
In this paper we prove that if X is an infinite class of flnite simple classical groups, then F2, the free group of rank 2, is residually X. This solves a special case of a question of W.Magnus. He conjectures that F2 is residually X for any infinite class X of finite non-abelian simple groups. 相似文献
9.
V. D. Mazurov 《Algebra and Logic》2000,39(3):189-198
We prove that a group which contains elements of orders 1, 2, 3, 4, 5 and does not contain elements of any other order is
locally finite and isomorphic either to an alternating group of degree 6 or to an extension of a nontrivial elementary Abelian
2-group by an alternating group of degree 5.
This article was written during my visit to the University of Manitoba, Canada, and supported by RFFR grant No. 99-01-00550.
Translated fromAlgebra i Logika, Vol. 39, No. 3, pp. 329–346, May–June, 2000. 相似文献
10.
We show the relative consistency of ℵ1 satisfying a combinatorial property considered by David Fremlin (in the question DU from his list) in certain choiceless
inner models. This is demonstrated by first proving the property is true for Ramsey cardinals. In contrast, we show that in
ZFC, no cardinal of uncountable cofinality can satisfy a similar, stronger property. The questions considered by D. H. Fremlin
are if families of finite subsets of ω1 satisfying a certain density condition necessarily contain all finite subsets of an infinite subset of ω1, and specifically if this and a stronger property hold under MA + ?CH. Towards this we show that if MA + ?CH holds, then for every family ? of ℵ1 many infinite subsets of ω1, one can find a family ? of finite subsets of ω1 which is dense in Fremlins sense, and does not contain all finite subsets of any set in ?.
We then pose some open problems related to the question.
Received: 2 June 1999 / Revised version: 2 February 2000 / Published online: 18 July 2001 相似文献
11.
Olga Macedońska 《代数通讯》2013,41(8):3661-3666
The paper concerns the question of A. Shalev: is it true that every collapsing group satisfies a positive law? We give a positive answer for groups in a large class C, including all soluble and residually finite groups. 相似文献
12.
It is proved that some groups with a strongly isolated 2-subgroup of period not exceeding four are locally finite. In particular,
the positive answer to Shunkov’s question 10.76 in the Kourovka notebook is obtained.
Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 272–285, August, 2000. 相似文献
13.
P. A. Zalesskii 《Monatshefte für Mathematik》2002,135(2):167-171
A profinite group is said to be just infinite if each of its proper quotients is finite. We address the question which profinite
groups admit just infinite quotients. It is proved that any profinite group whose order (as a supernatural number) is divisible
only by finitely many primes admits just infinite quotients. It is shown that if a profinite group G possesses the property in question then so does every open subgroup and every finite extension of G.
Received 20 July 2001 相似文献
14.
Carl Faith 《代数通讯》2013,41(9):4223-4226
This paper is on the subject of residually finite (= RF) modules and rings introduced by Varadarajan [93] and [98/99]. Specifically there are several theorems that simplify proofs and generalize some results of Varadarajan, namely. Theorem 1. An RF right R-module is finitely bedded (= has finite essential socle iff M is finite. Corollay. If T is a right RF woth just finitely many simple ringht R-modules, them R is fimite. Theorem 2. A commutative ring R is residually finite iff every local ring Rm at a maximal ideal m is finite. 相似文献
15.
L. Levai 《Israel Journal of Mathematics》1998,105(1):337-348
LetG be a residually finite or pro-finite group. We say thatG satisfies the linear core condition with constantc if all finite index (open) subgroups ofG contain a subgroup of index at mostc which is normal inG. Answering a question of L. Pyber we give a complete characterisation of finitely generated residually finite and pro-finite
groups satisfying a linear core generated residually finite and pro-finite groups satisfying a linear core condition. In the
case of infinitely generated groups we prove that such groups are abelian-by-finite.
Research supported by the Hungarian National Research Foundation (OTKA), grant no. 16432 and F023436. 相似文献
16.
Pavel Shumyatsky 《Israel Journal of Mathematics》2011,182(1):149-156
The following result is proved. Let n be a positive integer and G a residually finite group in which every product of at most 68 commutators has order dividing n. Then G′ is locally finite. 相似文献
17.
Summary Certain t* elements of an abstract algebra are called independent if every equation satisfied by these elements is identically
true in the algebra [2]. For finite algebras we have: Given an integert*>3, everyt* elements are independent if every operation oft* variables is trivial, i. e. if it is identically equal to one of the variables (Th. 1). Ift*≤3, then there exists an algebra in which everyt* elements are independent but not every operation oft* variables is trivial; moreover ift*=3, then n is the number of elements of such an algebra if n=2 or 4 (mod 6 and n>3 (Th. 2). 相似文献
18.
It is proved that any pseudovariety of finite semigroups generated by inverse semigroups, the subgroups of which lie in some
proper pseudovariety of groups, does not contain all aperiodic semigroups with commuting idempotents. In contrast we show
that every finite semigroup with commuting idempotents divides a semigroup of partial bijections that shares the same subgroups.
Finally, we answer in the negative a question of Almeida as to whether a result of Stiffler characterizing the semidirect
product of the pseudovarieties ofR-trivial semigroups and groups applies to any proper pseudovariety of groups. 相似文献
19.
K. Varadarajan 《Proceedings Mathematical Sciences》1999,109(4):345-351
Define a ringA to be RRF (resp. LRF) if every right (resp. left) A-module is residually finite. Refer to A as an RF ring if it is simultaneously
RRF and LRF. The present paper is devoted to the study of the structure of RRF (resp. LRF) rings. We show that all finite
rings are RF. IfA is semiprimary, we show thatA is RRF ⇔A is finite ⇔A is LRF. We prove that being RRF (resp. LRF) is a Morita invariant property. All boolean rings are RF. There are other infinite
strongly regular rings which are RF. IfA/J(A) is of bounded index andA does not contain any infinite family of orthogonal idempotents we prove:
IfA is one sided quasi-duo (left or right immaterial) not containing any infinite family of orthogonal idempotents then (i) and
(ii) are valid with the further strengthening thatA/J(A) is a finite product of finite fields. 相似文献
(i) | A an RRF ring ⇔ A right perfect andA/J(A) finite (henceA/J(A) finite semisimple artinian). |
(ii) | A an LRF ring ⇔ A left perfect andA/J(A) finite |
20.
Z. G. Khisamiev 《Algebra and Logic》2007,46(1):50-61
We study into a semilattice of numberings generated by a given fixed numbering via operations of completion and taking least
upper bounds. It is proved that, except for the trivial cases, this semilattice is an infinite distributive lattice every
principal ideal in which is finite. The least upper and the greatest lower bounds in the semilattice are invariant under extensions
in the semilattice of all numberings. Isomorphism types for the semilattices in question are in one-to-one correspondence
with pairs of cardinals the first component of which is equal to the cardinality of a set of non-special elements, and the
second — to the cardinality of a set of special elements, of the initial numbering.
Supported by INTAS grant No. 00-429.
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Translated from Algebra i Logika, Vol. 46, No. 1, pp. 83–102, January–February, 2007. 相似文献