共查询到20条相似文献,搜索用时 62 毫秒
1.
We prove that certain 1-relator groups have Property E. Using this fact, we characterize all conjugacy separable 1-relator groups of the form a,b;(a-αbβaαbγ)t , t 1, having residually finite outer automorphism groups. 相似文献
2.
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
3.
Koji Fujiwara 《Proceedings of the American Mathematical Society》2000,128(12):3463-3464
Farb and Masur showed that an irreducible lattice in a semisimple Lie group of rank at least two always has finite image by a homomorphism into the outer automorphism group of a closed, orientable surface group. We point out that their theorem extends to the outer automorphism groups of a certain class of torsion-free, freely indecomposable word-hyperbolic groups.
4.
We show first that certain automorphism groups of algebraic varieties, and even schemes, are residually finite and virtually
torsion free. (A group virtually has a property if some subgroup of finite index has it.) The rest of the paper is devoted
to a study of the groups of automorphisms. Aut(Γ) and outer automorphisms Out(Γ) of a finitely generated group Γ, by using
the finite-dimensional representations of Γ. This is an old idea (cf. the discussion of Magnus in [11]). In particular the
classes of semi-simplen-dimensional representations of Γ are parametrized by an algebraic varietyS
n
(Γ) on which Out(Γ) acts. We can apply the above results to this action and sometimes conclude that Out(Γ) is residually finite
and virtually torsion free. This is true, for example, when Γ is a free group, or a surface group. In the latter case Out(Γ)
is a “mapping class group.”
Partially supported by the NSF under Grant MCS 80-05802. 相似文献
5.
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
6.
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
7.
László Babai 《Discrete Mathematics》1974,8(1):13-20
If a class C of finite graphs is closed under contraction and forming subgraphs, and if every finite abstract group occurs as the automorphism group of some graph in C, then C contains all finite graphs (up to isomorphism). Also related results concerning automorphism groups of graphs on given surfaces are mentioned. 相似文献
8.
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
9.
We examine the palindromic automorphism group , of a free group F
n
, a group first defined by Collins in [5] which is related to hyperelliptic involutions of mapping class groups, congruence
subgroups of , and symmetric automorphism groups of free groups. Cohomological properties of the group are explored by looking at a contractible
space on which acts properly with finite quotient. Our results answer some conjectures of Collins and provide a few striking results about
the cohomology of , such as that its rational cohomology is zero at the vcd.
Received: January 17, 2000. 相似文献
10.
We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from
a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the
algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic
groups. We also construct examples of polycyclic-by-finite groups which have an automorphism group which does not contain
an arithmetic group of finite index. Finally we discuss applications of our results to the groups of homotopy self-equivalences
of K(Γ,1)-spaces and obtain an extension of arithmeticity results of Sullivan in rational homotopy theory. 相似文献
11.
Let G be any group and x an automorphism of G. The automorphism x is said to be nil if, for every g ∈ G, there exists n = n(g) such that [g, n x] = 1. If n can be chosen independently of g, we say that x is n-unipotent. A nil (resp. unipotent) automorphism x could also be seen as a left Engel element (resp. left n-Engel element) in the group G〈x〉. When G is a finite dimensional vector space, groups of unipotent linear automorphisms turn out to be nilpotent, so that one might ask to what extent this result can be extended to a more general setting. In this paper we study finitely generated groups of nil or unipotent automorphisms of groups with residual properties (e.g. locally graded groups, residually finite groups, profinite groups), proving that such groups are nilpotent. 相似文献
12.
Olga Varghese 《Archiv der Mathematik》2018,111(3):231-238
We show that certain representations over fields with positive characteristic of groups having CAT\((0)\) fixed point property \(\mathrm{F}\mathcal {B}_{\widetilde{A}_n}\) have finite image. In particular, we obtain rigidity results for representations of the following groups: the special linear group over \({\mathbb {Z}}\), \({\mathrm{SL}}_k({\mathbb {Z}})\), the special automorphism group of a free group, \(\mathrm{SAut}(F_k)\), the mapping class group of a closed orientable surface, \(\mathrm{Mod}(\Sigma _g)\), and many other groups. In the case of characteristic zero, we show that low dimensional complex representations of groups having CAT\((0)\) fixed point property \(\mathrm{F}\mathcal {B}_{\widetilde{A}_n}\) have finite image if they always have compact closure. 相似文献
13.
14.
Jérôme E. Los 《Topology》2004,43(1):49-69
Necessary and sufficient conditions (n.a.s.c) are found for a subgroup of the automorphism group of a finite graph to be realizable as the restriction to an invariant spine of some group of homeomorphisms of a compact surface. Also, n.a.s.c. are found for the restricted case when the surface is required to be orientable. The conditions are formulated in terms of the action of stabilizers of vertices on their stars. In both cases, a parametrization of the possible representations is given. Several examples are treated, as well as an application to deciding whether a given finite group of outer automorphisms of a free group is realizable via a surface homeomorphism. 相似文献
15.
This paper considers finite group actions on compact bordered surfaces — quotients of unbordered orientable surfaces under the action of a reflectional symmetry. Classification of such actions (up to topological equivalence) is carried out by means of the theory of non-euclidean crystallographic groups, and determination of normal subgroups of finite index in these groups, up to conjugation within their automorphism group. A result of this investigation is the determination, up to topological equivalence, of all actions of groups of finite order 6 or more on compact (orientable or non-orientable) bordered surfaces of algebraic genus p for 2≤p≤6. We also study actions of groups of order less than 6, or of prime order, on bordered surfaces of arbitrary algebraic genus p≥2. 相似文献
16.
F. K. Indukaev 《Moscow University Mathematics Bulletin》2007,62(6):219-227
For each positive integer N, an automorphism with the Reidemeister number 2N of the discrete Heisenberg group is constructed; an example of determination of points in the unitary dual object being fixed with respect to the mapping induced by the group automorphism is given. For wreath products of finitely generated Abelian groups and the group of integers, it is proved that if the Reidemeister number of an arbitrary automorphism is finite, then it is equal to the number of fixed points of the induced mapping on a finite-dimensional part of the unitary dual object. 相似文献
17.
Arthur Soulié 《代数通讯》2020,48(6):2467-2491
AbstractIn this paper, we deal with stable homology computations with twisted coefficients for mapping class groups of surfaces and of 3-manifolds, automorphism groups of free groups with boundaries and automorphism groups of certain right-angled Artin groups. On the one hand, the computations are led using semidirect product structures arising naturally from these groups. On the other hand, we compute the stable homology with twisted coefficients by FI-modules. This notably uses a decomposition result of the stable homology with twisted coefficients for pre-braided monoidal categories proved in this paper.Communicated by Jason P. Bell 相似文献
18.
O. V. Bryukhanov 《Siberian Mathematical Journal》2016,57(2):190-199
We give criteria for the fundamental groups of compact Sol-3-manifolds to be residually nilpotent and residually finite p-groups. 相似文献
19.
D. G. Khramtsov 《Algebra and Logic》1995,34(5):311-337
We prove that there exists an algorithm which solves a conjugacy problem for finite subgroups in automorphism and outer automorphism groups of a free group of finite rank. Of independent interest is the construction of an algorithm of decomposing an arbitrary free-by-finite group into a fundamental group of a finite graph of finite groups, with the number of steps evaluated explicitly. In passing, we solve the conjugacy problem for finite subgroups in almost free groups. As a consequence, an algorithm is obtained computing generating sets for a group of fixed points in an arbitrary finite automorphism group of a free group of finite rank.Translated fromAlgebra i Logika, Vol. 34, No. 5, pp. 558–606, September-October, 1995.Supported by the RFFR grant No. 93-011-1508 and by the ISF (International Science Foundation) grant RPC000. 相似文献
20.
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