共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
E. A. Tumanova 《Siberian Mathematical Journal》2017,58(3):546-552
Given a homomorphically closed root class K of groups, we find a criterion for a Baumslag–Solitar group to be a residually K-group. In particular, we establish that all Baumslag–Solitar groups are residually soluble and a Baumslag–Solitar group is residually finite soluble if and only if it is residually finite. 相似文献
3.
V. Metaftsis 《Journal of Pure and Applied Algebra》2010,214(8):1301-1305
We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable relatively hyperbolic group is residually finite. As a direct consequence, we obtain that the outer automorphism group of a limit group is residually finite. 相似文献
4.
We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable hyperbolic group
is residually finite. As a result, we are able to prove that the group of outer automorphisms of every finitely generated
Fuchsian group and of every free-by-finite group is residually finite. 相似文献
5.
设G是有限秩的剩余有限可解群或是有限秩的剩余有限可解群的有限扩张,α是G的一个索数p阶正则自同构且φ:G→G(g→[g,α])是满射,则G是幂零类不超过h(p)的幂零群,其中h(p)是只与p有关的函数. 相似文献
6.
Dan Segal 《Israel Journal of Mathematics》1996,94(1):1-5
We give an easy proof that a finitely generated group which is residually (finite and soluble of bounded rank) is nilpotent
by quasi-linear. This can be used to shorten the proofs of some recent theorems about residually finite groups. 相似文献
7.
D. I. Moldavanskii 《Ukrainian Mathematical Journal》1992,44(6):758-760
The paper examines the special case of the general construction of HNN-extensions of groups in which at least one of the associated subgroups is the base group. A criterion is determined for a group obtained in this way to be residually finite. Any group obtained as such an extension from a free nilpotent group of finite rank is residually finite.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 6, pp. 842–845, June, 1992. 相似文献
8.
D. N. Azarov 《Mathematical Notes》2013,93(3-4):503-509
A necessary and sufficient condition for the residual finiteness of a (generalized) free product of two residually finite solvable-by-finite minimax groups with cyclic amalgamated subgroups is obtained. This generalizes the well-known Dyer theorem claiming that every free product of two polycyclic-by-finite groups with cyclic amalgamated subgroups is a residually finite group. 相似文献
9.
D. N. Azarov 《Russian Mathematics (Iz VUZ)》2014,58(8):15-23
For soluble groups of finite rank we obtain the necessary and sufficient condition to be a virtually residually finite p-group. We also prove that a soluble group G of finite rank is residually π-finite for some finite set π of primes if and only if it has no subgroups of type Q and the torsion radical of G is a finite group. 相似文献
10.
D. T. Wise 《Commentarii Mathematici Helvetici》2001,76(2):314-338
It is proven that every positive one-relator group which satisfies the condition has a finite index subgroup which splits as a free product of two free groups amalgamating a finitely generated
malnormal subgroup. As a consequence, it is shown that every positive one-relator group is residually finite. It is shown that positive one-relator groups are generically and hence generically residually finite. A new method is given for recognizing malnormal subgroups of free groups. This method
employs a 'small cancellation theory' for maps between graphs.
Received: August 4, 2000 相似文献
11.
Jacob Mostovoy 《Archiv der Mathematik》2019,113(3):229-235
We show that for each
$$n\in {\mathbb {N}}$$
the pure cactus group
$$\Gamma _{n+1}$$
embeds into a right-angled Coxeter group and, therefore, is residually nilpotent. In addition, we construct an explicit residually torsion-free nilpotent subgroup of finite index in
$$\Gamma _{n+1}$$
. 相似文献
12.
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
13.
Grossman first showed that outer automorphism groups of 1-relator groups given by orientable surface groups are residually finite, whence mapping class groups of orientable surfaces are residually finite. Allenby, Kim and Tang showed that outer automorphism groups of cyclically pinched 1-relator groups are residually finite, whence mapping class groups of orientable and non-orientable surfaces are residually finite. In this paper we show that outer automorphism groups of certain conjugacy separable 1-relator groups are residually finite. 相似文献
14.
J. O. Button 《Israel Journal of Mathematics》2008,167(1):111-140
We prove that if a group possesses a deficiency 1 presentation where one of the relators is a commutator, then it is ℤ × ℤ,
large or is as far as possible from being residually finite. Then we use this to show that a mapping torus of an endomorphism
of a finitely generated free group is large if it contains a ℤ × ℤ subgroup of infinite index, as well as showing that such
a group is large if it contains a Baumslag-Solitar group of infinite index and has a finite index subgroup with first Betti
number at least 2. We give applications to free by cyclic groups, 1 relator groups and residually finite groups. 相似文献
15.
S. Dobrynin 《Journal of Mathematical Sciences》2001,107(5):4161-4165
It is proved that the Hall group (a solvable, not residually finite group of solvability length 3) can be locally embedded into the class of finite groups. Bibliography: 2 titles. 相似文献
16.
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
17.
For a word of a free group of rank n , the author obtains an invariant called its standard exponent, and shows that if any residually finite group satisfying the law defined by such a word is almost nilpotent, then the standard exponent of the word equals 1 . Conversely, if the standard exponent of a word ω is 1 , then any residually finite or soluble group and any locally finite or soluble group satisfying the group law ω≡ 1 is nilpotent-of-bounded-class-by-bounded-exponent. 相似文献
18.
D. N. Azarov 《Russian Mathematics (Iz VUZ)》2017,61(5):1-6
Let p be a prime number. Recall that a group G is said to be a residually finite p-group if for every non-identity element a of G there exists a homomorphism of the group G onto a finite p-group such that the image of a does not coincide with the identity. We obtain a necessary and sufficient condition for the free product of two residually finite p-groups with finite amalgamated subgroup to be a residually finite p-group. This result is a generalization of Higman’s theorem on the free product of two finite p-groups with amalgamated subgroup. 相似文献
19.
We describe elementary examples of finitely presented sofic groups which are not residually amenable (and thus not initially subamenable or LEA, for short). We ask if an amalgam of two amenable groups over a finite subgroup is residually amenable and answer this positively for some special cases, including countable locally finite groups, residually nilpotent groups and others. 相似文献
20.
The paper describes methods of constructing of residually connected and flag-transitive geometries and corresponding presentations cf finite groups. The methods are illustrated on the finite simple group U4(2). As a result all residually connected and flag-transitive geometries of the group U4(2) with maximsl subgroups as the stabilizers of geometries' elements (exclsding rank 4 geometries with a trivial Borel subgroup) were described. USing these geometries several "natural" presentations of the group U4(2) were obtained. 相似文献