共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we prove a limit set intersection theorem in relatively hyperbolic groups. Our approach is based on a study
of dynamical quasiconvexity of relatively quasiconvex subgroups. Using dynamical quasiconvexity, many well-known results on
limit sets of geometrically finite Kleinian groups are derived in general convergence groups. We also establish dynamical
quasiconvexity of undistorted subgroups in finitely generated groups with nontrivial Floyd boundaries. 相似文献
2.
Given a group acting cellularly and cocompactly on a simply connected 2-complex, we provide a criterion establishing that all finitely generated subgroups have quasiconvex orbits. This work generalizes the “perimeter method”. As an application, we show that high-powered one-relator products A∗B/《rn》 are coherent if A and B are coherent. 相似文献
3.
Paul E. Schupp 《Geometriae Dedicata》2003,96(1):179-198
We show that all groups in a very large class of Coxeter groups are locally quasiconvex and have a uniform membership problem solvable in quadratic time. If a group in the class satisfies a further hypothesis it is subgroup separable and relevant homomorphisms are also calculable in quadratic time. The algorithm also decides if a finitely generated subgroup has finite index. 相似文献
4.
Yury Semenov 《代数通讯》2013,41(15):6323-6347
Abstract We define quasiconvexity cone Qcone(τ) over an infinite hyperbolic (in the sense of Gromov) group τ as the set of conjugacy classes of infinite quasiconvex subgroups H?τ and show that the abelian group of Qcone(τ)-divisors, i.e. finite sums of points from Qcone(τ) with integer coefficients, can be equipped with a natural structure of commutative associative ring with identity. Euler characteristic can be considered as a rational-valued function on Qcone(τ). This approach gives another point of view on the strengthened form of Hanna Neumann's conjecture on the maximal rank of the intersection of two finitely generated subgroups of the free group on two generators. 相似文献
5.
We define a new notion of sectional curvature for 2-complexes,
and describe a variety of examples with nonpositive or negative sectional
curvature. The 2-complexes with nonpositive sectional curvature have coherent
and locally indicable fundamental groups. The 2-complexes with
negative sectional curvature have the compact core property for covers
with finitely generated fundamental group. The fundamental groups of
compact 2-complexes with metric negative sectional curvature have locally-quasiconvex
fundamental groups. 相似文献
6.
Frédéric Haglund 《Advances in Mathematics》2010,224(5):1890-1903
In this paper we prove that every finitely generated Coxeter group has a finite index subgroup that is the fundamental group of a special cube complex. Some consequences include: Every f.g. Coxeter group is virtually a subgroup of a right-angled Coxeter group. Every word-hyperbolic Coxeter group has separable quasiconvex subgroups. 相似文献
7.
D. V. Artamonov 《Mathematical Notes》2007,81(5-6):573-589
A natural criterion for dimensional full-valuedness of locally compact spaces with finitely generated local homology is given. 相似文献
8.
We study notions such as finite presentability and coherence, for partially ordered abelian groups and vector spaces. Typical results are the following: (i) A partially ordered abelian group G is finitely presented if and only if G is finitely generated as a group, G + is well-founded as a partially ordered set, and the set of minimal elements of G +\ {0} is finite. (ii) Torison-free, finitely presented partially ordered abelian groups can be represented as subgroups of some Zn , with a finitely generated submonoid of (Z+)n as positive cone. (iii) Every unperforated, finitely presented partially ordered abelian group is Archimedean. Further, we establish connections with interpolation. In particular, we prove that a divisible dimension group G is a directed union of simplicial subgroups if and only if every finite subset of G is contained into a finitely presented ordered subgroup. 相似文献
9.
《Optimization》2012,61(3-4):219-228
It was recently shown by Nikodem that a function defined on an open convex subset of R n is convex if and only if it is midpoint convex and quasiconvex. It is shown that quasiconvexity can be replaced by strict quasiconvexity and that the openness condition can be removed altogether. The domain can then be taken from a general real linear space. There will also be given some related results of a “local” nature 相似文献
10.
In answer to a question of Myasnikov, we show that there exist hyperbolic groups for which there is no algorithm to decide
which finitely generated subgroups are malnormal or quasiconvex.
Bridson’s research is supported by an EPSRC Advanced Fellowship and Wise is supported in part by a grant from the NSF. 相似文献
11.
Stephen J. Pride 《代数通讯》2013,41(10):3525-3536
Let ? be an additive category and 𝒞 a full subcategory with split idempotents, and closed under isomorphic images and finite direct sums. We give conditions on ? and 𝒞 implying that ? embeds into an abelian category, so that the objects of 𝒞 turn into injective objects. This construction generalizes the embedding of exactly definable categories into locally coherent categories, while the dual construction generalizes the embedding of finitely accessible categories into Grothendieck categories with a family of finitely generated projective generators. As applications, we characterize exactly definable categories through intrinsic properties and study those locally coherent categories whose fp-injective objects form a Grothendieck category. 相似文献
12.
13.
A group is called metahamiltonian if all its non-abelian subgroups are normal; it is known that locally soluble metahamiltonian groups have finite derived
subgroup. This result is generalized here, by proving that every locally graded group with finitely many derived subgroups
of non-normal subgroups has finite derived subgroup. Moreover, locally graded groups having only finitely many derived subgroups
of infinite non-normal subgroups are completely described.
Received: 25 April 2005 相似文献
14.
We study finite extension groups of lattices in Lie groups which have finitely many connected components. We show that every non-cocompact Fuchsian group (these are the non-cocompact lattices in ) has an extension group of finite index which is not isomorphic to a lattice in a Lie group with finitely many connected components. On the other hand we prove that these are, in an appropriate sense, the only lattices in Lie groups which have extension groups of this kind. We also show that an extension group of finite index of a lattice in a Lie group with finitely many connected components has only finitely many conjugacy classes of finite subgroups. To cite this article: F. Grunewald, V. Platonov, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
15.
《Optimization》2012,61(4):309-318
A kind of generalized convex functions is said to be stable with respect to some property (P) if this property is maintaincd during an arbitrary function from this class is disturbed by a linear functional with sufficiently small norm. Unfortunately. known generallzed convexities iike quasicunvexity, explicit quasiconvexity. and pseudoconvexity are not stable with respect to such optimization properties which are expected to be true by these generalizations, even if the domain ol the functions is compact. Therefore, we introduce the notion of s-quasiconvex functions. These functions are quasiconvex, explicitly quasicon vex. and pseudoconvex if they are continuously differentiable. Especially, the s-quasiconvexity is stable with respect to the following important properties: (Pl) all lower level sets are convex, (P2) each local minimum is a global minimum. and (P3) each stationary point is a global minimizer. In this paper, different aspects. of s–quasiconvexity and its stability are investigated. 相似文献
16.
Daniel T. Wise 《Proceedings of the American Mathematical Society》2008,136(1):41-48
We give a criterion for the nonpositive sectional curvature of -complexes. As a consequence, we show that certain -complexes have locally indicable, coherent and even locally quasiconvex fundamental groups.
17.
We define and study the class of positively finitely related (PFR) profinite groups. Positive finite relatedness is a probabilistic property of profinite groups which provides a first step to defining higher finiteness properties of profinite groups which generalize the positively finitely generated groups introduced by Avinoam Mann. We prove many asymptotic characterisations of PFR groups, for instance we show the following: a finitely presented profinite group is PFR if and only if it has at most exponential representation growth, uniformly over finite fields (in other words: the completed group algebra has polynomial maximal ideal growth). From these characterisations we deduce several structural results on PFR profinite groups. 相似文献
18.
19.
Using the notion of fibers, where two rays belong to the same fiber if and only if they lie within bounded Hausdorff‐distance of one another, we study how many fibers of a graph contain a geodetic ray and how many essentially distinct geodetic rays such “geodetic fibers” must contain. A complete answer is provided in the case of locally finite graphs that admit an almost transitive action by some infinite finitely generated, abelian group. Such graphs turn out to have either finitely many or uncountably many geodetic fibers. Furthermore, with finitely many possible exceptions, each of these fibers contains uncountably many geodetic rays. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 67–88, 2000 相似文献
20.
Olga Varghese 《Discrete Mathematics》2019,342(7):2100-2105
Graph products of groups and Coxeter groups are defined via vertex-edge-labeled graphs. We show that if the graph has a special shape, then the corresponding group is coherent, i.e. every finitely generated subgroup is finitely presented. 相似文献