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1.
A subgroupX of the locally finite groupG is said to beconfined, if there exists a finite subgroupF≤G such thatX
g∩F≠1 for allg∈G. Since there seems to be a certain correspondence between proper confined subgroups inG and non-trivial ideals in the complex group algebra ℂG, we determine the confined subgroups of periodic simple finitary linear groups in this paper.
Dedicated to the memory of our friend and collaborator Richard E. Phillips 相似文献
2.
We show for a finite abelian groupG and any element in the image of the Swan homomorphism sw:
that it can be realized as the finiteness obstruction of a finitely dominated connectedCW-complexX with fundamental group π1(X) =G such that π1(X) is equal to the subgroupG
1(X) defined by Gottlieb. This is motivated by the observation that anyH-spaceX satisfies π1(X) =G
1(X) and still the problem is open whether any finitely dominatedH-space is up to homotopy finite. 相似文献
3.
V. N. Berestovskii 《Mathematical Notes》1995,58(3):905-909
We prove that a homogeneous effective spaceM=G/H, whereG is a connected Lie group andH⊂G is a compact subgroup, admits aG-invariant Riemannian metric of positive Ricci curvature if and only if the spaceM is compact and its fundamental group π1(M) is finite (in this case any normal metric onG/H is suitable). This is equivalent to the following conditions: the groupG is compact and the largest semisimple subgroupLG⊂G is transitive onG/H. Furthermore, ifG is nonsemisimple, then there exists aG-invariant fibration ofM over an effective homogeneous space of a compact semisimple Lie group with the torus as the fiber.
Translated fromMatematicheskie Zametki, Vol. 58, No. 3, pp. 334–340, September, 1995. 相似文献
4.
A. Leibman 《Israel Journal of Mathematics》2002,129(1):29-60
A mapping ϕ of a groupG to a groupF is said to be polynomial if it trivializes after several consecutive applications of operatorsD
h
,h ∈G, defined byD
h
ϕ(g)=ϕ(g)
−1
ϕ(gh). We study polynomial mappings of groups, mainly to nilpotent groups. In particular, we prove that polynomial mappings to
a nilpotent group form a group with respect to the elementwise multiplication, and that any polynomial mappingG→F to a nilpotent groupF splits into a homomorphismG→G’ to a nilpotent groupG’ and a polynomial mappingG’→F. We apply the obtained results to prove the existence of the compact/weak mixing decomposition of a Hilbert space under a
unitary polynomial action of a finitely generated nilpotent group.
This work was supported by NSF, Grants DMS-9706057 and 0070566. 相似文献
5.
Gilbert Levitt 《Commentarii Mathematici Helvetici》1994,69(1):28-38
LetG be a finitely generated group acting on anR-treeT. First assume that the action is free, and minimal (there is no proper invariant subtree), or more generally that it satisfies
a certain finiteness condition. Then it may be described as agraph of transitive actions: the action may be recovered from a finite graph, together with additional data; in particular, every vertexv carries an action (G
v, Tv) whose orbits are dense. For the action (G, T), it follows for instance that the closure of any orbit is a discrete union of closed subtrees: it cannot meet a segment
in a Cantor set.
Now let ℓ be the length function for an arbitrary action ofG. For ɛ>0 small enough, the subgroupG(ɛ)⊂G generated by elementsg withg is independent of ɛ, andG/G(ɛ) is free. Several interpretations are given for the rank ofG/G(ɛ). 相似文献
6.
Let F n be the free group of rank n, and let Aut+(F n ) be its special automorphism group. For an epimorphism π : F n → G of the free group F n onto a finite group G we call the standard congruence subgroup of Aut+(F n ) associated to G and π. In the case n = 2 we fully describe the abelianization of Γ+(G, π) for finite abelian groups G. Moreover, we show that if G is a finite non-perfect group, then Γ+(G, π) ≤ Aut+(F 2) has infinite abelianization. 相似文献
7.
Atournament regular representation (TRR) of an abstract groupG is a tournamentT whose automorphism group is isomorphic toG and is a regular permutation group on the vertices ofT. L. Babai and W. Imrich have shown that every finite group of odd order exceptZ
3 ×Z
3 admits a TRR. In the present paper we give several sufficient conditions for an infinite groupG with no element of order 2 to admit a TRR. Among these are the following: (1)G is a cyclic extension byZ of a finitely generated group; (2)G is a cyclic extension byZ
2n+1 of any group admitting a TRR; (3)G is a finitely generated abelian group; (4)G is a countably generated abelian group whose torsion subgroup is finite. 相似文献
8.
Gordan Savin 《Israel Journal of Mathematics》1992,80(1-2):195-205
LetG andH ⊂G be two real semisimple groups defined overQ. Assume thatH is the group of points fixed by an involution ofG. Letπ ⊂L
2(H\G) be an irreducible representation ofG and letf επ be aK-finite function. Let Γ be an arithmetic subgroup ofG. The Poincaré seriesP
f(g)=ΣH∩ΓΓ
f(γ{}itg) is an automorphic form on Γ\G. We show thatP
f is cuspidal in some cases, whenH ∩Γ\H is compact.
Partially supported by NSF Grant # DMS 9103608. 相似文献
9.
Dan Segal 《Israel Journal of Mathematics》1996,94(1):7-19
A groupG hasweak polynomial subgroup growth (wPSG) of degree ≤α if each finite quotient Ḡ ofG contains at most │Ḡ│
a
subgroups. The main result is that wPSG of degree α implies polynomial subgroup growth (PSG) of degree at mostf(α). It follows that wPSG is equivalent to PSG. A corollary is that if, in a profinite groupG, thek-generator subgroups have positive “density” δ, thenG is finitely generated (the number of generators being bounded by a function ofk and δ). 相似文献
10.
H. A. Jung 《Combinatorica》1981,1(3):285-288
Results involving automorphisms and fragments of infinite graphs are proved. In particular for a given fragmentC and a vertex-transitive subgroupG of the automorphism group of a connected graph there exists σ≠G such that σ[C] ⊂C. This proves the countable case of a conjecture of L. Babai and M. E. Watkins concerning graphs allowing a vertex-transitive
torsion group action.
Dedicated to Prof. K. Wagner on his 70th birthday 相似文献
11.
T. Hamachi 《Israel Journal of Mathematics》1997,100(1):249-283
Given a pair of an ergodic measured discrete equivalence relationR and a subrelationS ⊂R of finite index, a classification of the inclusion up to orbit equivalence will be discussed. In case of amenable and type
III0 relations, the orbit equivalence classes of inclusions will be completely classified in terms of a collection of a subgroupH and a normal subgroupG
0 of a finite groupG and an ergodic group (G/G
0) extension of a nonsingular flow. This is a generalization of Krieger’s theorem by which orbit equivalence classes of single
relations were classified. Due to this result, essential type III inclusions will be made clear.
Supported by the Japan Ministry of Education, Grant-in-Aid for Scientific Research No. (C)07640223.
An erratum to this article is available at . 相似文献
12.
B. A. F. Wehrfritz 《Israel Journal of Mathematics》1984,47(2-3):154-164
LetD=F(G) be a division ring generated as a division ring by its central subfieldF and the polycyclic-by-finite subgroupG of its multiplicative group, letn be a positive integer and letX be a finitely generated subgroup of GL(n, D). It is implicit in recent works of A. I. Lichtman thatX is residually finite. In fact, much more is true. If charD=p≠0, then there is a normal subgroup ofX of finite index that is residually a finitep-group. If charD=0, then there exists a cofinite set π=π(X) of rational primes such that for eachp in π there is a normal subgroup ofX of finite index that is residually a finitep-group. 相似文献
13.
Juan Pablo Navarrete Waldemar Barrera 《Bulletin of the Brazilian Mathematical Society》2009,40(1):99-106
In this paper, we prove following: If G ⊂ PU (2, 1) is an infinite, discrete group, acting on Pℂ2 without complex invariant lines, then the component containing ℍPℂ2 of the domain of discontinuity Ω(G) = PPℂ2∖ Λ (G), according to Kulkarni, is G-invariant complete Kobayashi hyperbolic.
The authors were supported by the Universidad Autónoma de Yucatán and the Universidad Nacional Autónoma de México. 相似文献
14.
M. S. Raghunathan 《Proceedings Mathematical Sciences》1989,99(2):127-146
It is shown in this paper that ifG is the group ofk-points of a semisimple algebraic groupG over a local fieldk of positive characteristic such that all itsk-simple factors are ofk-rank 1 and Γ ⊂G is a non-cocompact irreducible lattice then Γ admits a fundamental domain which is a union of translates of Siegel domains.
As a consequence we deduce that ifG has more than one simple factor, then Γ is finitely generated and by a theorem due to Venkataramana, it is arithmetic. 相似文献
15.
A. N. Starkov 《Mathematical Notes》1995,58(1):744-751
Ergodic one-parameter flows (G/Γ,g
ℝ) induced by the left action of a subgroupg
ℝ ⊂G on homogeneous spaces of finite volume are considered. Letℳ ⊂ ℝ+ be the set of allt>0 such that the cascade (G/Γ,g
t
ℤ) is metrically isomorphic to the cascade (G/Γ,g
ℤ). We prove that eitherℳ is at most countable or the subgroupg
ℝ is horocyclic andℳ=ℝ+. We prove that a metric isomorphism of ergodic quasi-unipotent cascades (or flows) is affine on almost all fibers of a certain
natural bundle. The result generalizes Witte's theorem on the affinity of such isomorphisms of cascades with the mixing property;
this is applied to the study of the structure of the setℳ ⊂ ℝ+. The proof is based on the fundamental Ratner theorem stating that the ergodic measures of unipotent cascades are algebraic.
Translated fromMatematicheskie Zametki, Vol. 58, No. 1, pp. 98–110, July, 1995.
This research was partially supported by the Russian Foundation for Basic Research under grant No. 94-01-00082a and by the
International Science Foundation. 相似文献
16.
Michael L. Mihalik 《Commentarii Mathematici Helvetici》1996,71(1):362-372
If a finitely presented groupG is negatively curved, automatic or asynchronously automatic thenG has an asynchronously bounded “almost prefix closed” combing. Results in [Br1] and [E] imply that the fundamental group of any closed 3-manifold satisfying Thurston's geometrization conjecture has an
asynchronously bounded, almost prefix closed combing.
MAIN THEOREM. IfM is a compactP
2-irreducible 3-manifold,π
1 (M) has an asynchronously bounded, almost prefix closed combing, andH, a subgroup ofπ
1 (M), is quasiconvex with respect to this combing, then the cover ofM corresponding toH is a missing boundary manifold. 相似文献
17.
Gerhard Behrendt 《Graphs and Combinatorics》1992,8(3):203-206
For a graph Ф letF(Ф) be the class of finite graphs which do not contain an induced subgraph isomorphic to Ф. We show that whenever Ф is not
isomorphic to a path on at most 4 vertices or to the complement of such a graph then for every finite groupG there exists a graph ГєF(Ф) such thatG is isomorphic to the automorphism group of Г. For all paths д on at most 4 vertices we determine the class of all automorphism
groups of members ofF(д). 相似文献
18.
Edmond E. Granirer 《Israel Journal of Mathematics》1990,69(3):321-336
LetG ⊂ Aut ℳ be a countable group, ℳ a Von Neumann algebra. LetE be a set of pure states on ℳ such thatG*E ⊂E, S
G be the set ofG invariant states on ℳ andS
E
G
=S
G ∩w* cl coE. We investigate in this paper some geometric properties for the setS
E
G
which turn out to be equivalent to amenability for the groupG. For example, we show thatS
E
G
⊂ ℳ* (S
E
G
has the WRNP) implies that ℳ contains minimal projections (ê containsfinite G invariant orbits) hold true, for all ℳ iffG is amenable. Furthermore we show that ifG is amenable thenS
G ∩M
*
⊥
contains a big set, thus improving results obtained by Ching Chou in [2]. These results imply that no action of an amenable
countable groupG on an arbitraryW* algebra ℳ iss — strongly ergodic. Moreover cardS
G ∩M
*
⊥
≧2
c
(see M. Choda [4], K. Schmidt [21] and compare with A. Connes and B. Weiss [5]).
The author gratefully acknowledges the support of an Izaak Walton Killam Memorial Senior Fellowship. 相似文献
19.
Andrea Lucchini 《Israel Journal of Mathematics》2011,181(1):53-64
It has been conjectured by Mann that the infinite sum Σ
H
μ(H,G)/|G:H|
s
, where H ranges over all open subgroups of a finitely generated profinite group G, converges absolutely in some half right plane if G is positively finitely generated. We prove that the conjecture is true if the nonabelian crowns of G have bounded rank. In particular Mann’s conjecture holds if G has polynomial subgroup growth or is an adelic profinite group. 相似文献
20.
Pekka Tukia 《Journal d'Analyse Mathématique》2006,99(1):35-87
We extend the results of [T2] to the situation where there is a compatibility with the action of a Kleinian group. A classical
Techmüller sequence is a sequence of quasiconformal mapsf
i with complex dilatations of the form
, where ϕ is a quadratic differential and 0<-k
i<1 are numbers such thatk
i→1 asi→∞. We proved in [T2] that if τ is a vertical trajectory associated to ϕ, then there is often, for instance if the sequence
is normalized so thatf
i fix 3 points, a subsequence such thatf
i tend either toward a constant or an injective map of τ. If there is compatibility with the action of a non-elementary finitely
generated Kleinian groupG, we can given a precise characterization which of these cases occurs. Suppose thatf
i induce isomorphisms ϕi ofG onto another Kleinian group and that ϕi have algebraic limit ϕ. If the quadratic differential is defined on a component of the ordinary set ofG, if there are no parabolic elements, and if τ is extended maximally so that all branches coming together at a singular point
are included, then we can state the main result as follows. The limit is a constantc if the stabilizerG
τ of τ is elementary; and, if it is non-elementary, then the limit is injective. In the first case, ϕ(g) is parabolic with fixpointc wheneverg∈G
τ is of infinite order; and in the latter case, the limitf is an embedding of τ in a natural topology of τ, andf embeds τ into a component of the limit set of ϕG whose stabilizer is ϕG
τ. Various extensions and generalizations are presented.
The research for this paper has been supported by the project 51749 of the Academy of Finland. 相似文献