共查询到20条相似文献,搜索用时 13 毫秒
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Coulbois Thierry; Hilion Arnaud; Lustig Martin 《Journal London Mathematical Society》2008,78(3):755-766
We study the map which associates to a current its support (whichis a lamination). We show that this map is Out(FN)-equivariant,not injective, not surjective and not continuous. However itis semi-continuous and almost surjective in a suitable sense.Given an -tree T (with dense orbits) in the boundary of outerspace and a current µ carried by the dual lamination ofT, we define a dual pseudo-distance dµ on T. When thetree and the current come from a measured geodesic laminationon a surface with boundary, the dual distance is the originaldistance of the tree T. In general, such a good correspondencedoes not occur. We prove that when the tree T is the attractivefixed point of a non-geometric irreducible, with irreduciblepowers, outer automorphism, the dual lamination of T is uniquelyergodic and the dual distance dµ is either zero or infinitethroughout T. 相似文献
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Eng Tjioe Tan 《manuscripta mathematica》1988,60(4):477-486
Recent results on the Gupta representation of the unique stem cover of a free Bieberbach group lead to explicite determination of its Schur multiplicator. The aim of this note is to estimate the free-abelian rank of the Schur multiplicator, using only the 8-term Eckmann-Hilton-Stammbach exact homology sequence induced by the free Bieberbach group modulo its nontrivial center. The note ends with a discussion about the structure of torsion-free Bieberbach groups constructed by S.Rosset. 相似文献
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Longyun Ding 《Topology and its Applications》2007,154(2):410-420
We define some new metrics on free groups and obtain a class of Polish groups by taking appropriate metric completions so that every Polish group is the quotient group of some one in the class. Moreover, we show that the resulting groups can be taken to be Polishable subgroups of the infinite permutation group S∞. 相似文献
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Daniel T. Wise 《Israel Journal of Mathematics》2012,191(1):337-345
We show that for each finitely generated infinite index subgroup H of a free group F, there is a proper cocompact action of F on a CAT(0) cube complex with a single orbit of hyperplane stabilized by conjugates of H. 相似文献
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Mathematische Annalen - 相似文献
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Myoungho Moon 《Proceedings of the American Mathematical Society》2000,128(7):1885-1892
Let be either a free product with amalgamation or an HNN group where is isomorphic to a free abelian group of finite rank. Suppose that both and have no nontrivial, finitely generated, normal subgroups of infinite indices. We show that if contains a finitely generated normal subgroup which is neither contained in nor free, then the index of in is finite. Further, as an application of this result, we show that the fundamental group of a torus sum of -manifolds and , the interiors of which admit hyperbolic structures, have no nontrivial, finitely generated, nonfree, normal subgroup of infinite index if each of and has at least one nontorus boundary.
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Published in Algebra i Logika, Vol. 29, No. 6, pp. 746–751, November–December, 1990. 相似文献
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D. G. Khramtsov 《Algebra and Logic》2005,44(2):117-131
It is proved that any non-trivial endomorphism of an automorphism group AutFn of a free group Fn, for n 3, either is an automorphism or factorization over a proper automorphism subgroup. An endomorphism of AutF2 is an automorphism, or else a homomorphism onto one of the groups S3, D8, Z2 × Z2, Z2, or
(Z2 × Z2). A non-trivial homomorphism of AutFn into AutFm, for n 3, m 2, and n > m, is a homomorphism onto Z2 with kernel SAutFn. As a consequence, we obtain that AutFn is co-Hopfian.Supported by RFBR grant No. 02-01-00293 and by the Council for Grants (under RF President) and State Aid of Fundamental Science Schools, project NSh-2069.2003.1.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 211–237, March–April, 2005. 相似文献
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We give a topological framework for the study of Sela'slimit groups: limit groups are limits of free groups in a compact space of marked groups. Many results get a natural interpretation in
this setting. The class of limit groups is known to coincide with the class of finitely generated fully residually free groups.
The topological approach gives some new insight on the relation between fully residually free groups, the universal theory
of free groups, ultraproducts and non-standard free groups. 相似文献
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D. G. Khramtsov 《Mathematical Notes》1985,38(3):721-724
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Let F m be the free group on m generators, and let G be a finite nilpotent group of non square-free order; we show that for each m ≥ 2 the integral group ring Z[G × F m ] has infinitely many stably free modules of rank 1. 相似文献
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We prove that in the category of pro-p groups any finitely generated group G with a free open subgroup splits either as an amalgamated free product or as an HNN-extension over a finite p-group. From this result we deduce that such a pro-p group is the pro-p completion of a fundamental group of a finite graph of finite p-groups. 相似文献
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E. A. Mikhailyuk 《Ukrainian Mathematical Journal》1991,43(7-8):1047-1051
With each subgroup A of a free group F there is associated a number FA called the quasi-index. It is proved that FA=ªA¦ if ¦FA¦ is finite. Some properties of the quasi-index are also established, in particular that the analog of Lagrange's theorem is valid for it: FB FA AB if A B as well as generalizations of Howson's and Byrnes' theorems.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 1115–1119, July–August, 1991. 相似文献
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A. Savchenko 《Topology and its Applications》2010,157(4):724-729
We consider ultrametrizations of free topological groups of ultrametric spaces. A construction is defined that determines a functor in the category UMET1 of ultrametric spaces of diameter ?1 and nonexpanding maps. This functor is the functorial part of a monad in UMET1 and we provide a characterization of the category of its algebras. 相似文献
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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