共查询到20条相似文献,搜索用时 15 毫秒
1.
V. Roman’kov 《Journal of Pure and Applied Algebra》2011,215(4):664-671
Let N be a finitely generated nilpotent group. We show that there is an algorithm that for any automorphism φ∈Aut(N) computes its Reidemeister number R(φ). It is proved that any free nilpotent group Nrc of rank r and class c belongs to class R∞ if any of the following conditions holds: r=2 and c≥4; r=3 and c≥12; r≥4 and c≥2r. 相似文献
2.
Vladimir Tolstykh 《Journal of Pure and Applied Algebra》2011,215(9):2086-2098
Let F be an infinitely generated free group and let R be a fully invariant subgroup of F such that (a) R is contained in the commutator subgroup F′ of F and (b) the quotient group F/R is residually torsion-free nilpotent. Then the automorphism group of the group F/R′ is complete. In particular, the automorphism group of any infinitely generated free solvable group of derived length at least two is complete.This extends a result by Dyer and Formanek (1977) [7] on finitely generated groups Fn/R′ where Fn is a free group of finite rank n at least two and R a characteristic subgroup of Fn. 相似文献
3.
A Hausdorff topological group G is minimal if every continuous isomorphism f:G→H between G and a Hausdorff topological group H is open. Significantly strengthening a 1981 result of Stoyanov, we prove the following theorem: For every infinite minimal abelian group G there exists a sequence of cardinals such that
4.
P. Christopher Staecker 《Topology and its Applications》2010,157(10-11):1736-1741
We give an easily checkable algebraic condition which implies that two elements of a finitely generated free group are members of distinct doubly-twisted conjugacy classes with respect to a pair of homomorphisms. We further show that this criterion is satisfied with probability 1 when the homomorphisms and elements are chosen at random. 相似文献
5.
Mikhail Tkachenko 《Topology and its Applications》2009,156(7):1298-1305
We show that a Hausdorff paratopological group G admits a topological embedding as a subgroup into a topological product of Hausdorff first-countable (second-countable) paratopological groups if and only if G is ω-balanced (totally ω-narrow) and the Hausdorff number of G is countable, i.e., for every neighbourhood U of the neutral element e of G there exists a countable family γ of neighbourhoods of e such that ?V∈γVV−1⊆U. Similarly, we prove that a regular paratopological group G can be topologically embedded as a subgroup into a topological product of regular first-countable (second-countable) paratopological groups if and only if G is ω-balanced (totally ω-narrow) and the index of regularity of G is countable.As a by-product, we show that a regular totally ω-narrow paratopological group with countable index of regularity is Tychonoff. 相似文献
6.
Çetin Vural 《Topology and its Applications》2008,155(12):1329-1331
Let G be a paratopological group which is a GO-space. We have showed that if the multiplication in G preserves the order on G, then G is paracompact. 相似文献
7.
IfM is a closed Nil geometry 3-manifold then 1(M) is almost convex with respect to a fairly simple geometric generating set. IfG is a central extension or a extension of a word hyperbolic group, thenG is also almost convex with respect to some generating set. Combining these with previously known results shows that ifM is a closed 3-manifold with one of Thurston's eight geometries, 1(M) is almost convex with respect to some generating set if and only if the geometry in question is not Sol. 相似文献
8.
B.A.F. Wehrfritz 《Journal of Pure and Applied Algebra》2007,209(2):301-309
Let D be a division ring of finite degree d and let n be a positive integer. If G is any soluble subgroup of , we prove that G has derived length at most
9+log2d+(11/3)log2n 相似文献
9.
For A an Archimedean Riesz space (=vector lattice) with distinguished positive weak unit eA, we have the Yosida representation  as a Riesz space in D(XA), the lattice of extended real valued functions on the space of eA-maximal ideas. This note is about those A for which  is a convex subset of D(XA); we call such A “convex”.Convex Riesz spaces arise from the general issue of embedding as a Riesz ideal, from consideration of uniform- and order-completeness, and from some problems involving comparison of maximal ideal spaces (which we won't discuss here; see [10]).The main results here are: (2.4) A is convex iff A is contained as a Riesz ideal in a uniformly complete Φ-algebra B with identity eA. (3.1) Any A has a convex reflection (i.e., embeds into a convex B with a universal mapping property for Riesz homomorphisms; moreover, the embedding is epic and large). 相似文献
10.
§ 1 IntroductionLet N be the set of all natural numbers.Write Z+=N∪ { 0 } ,Nn={ 1 ,2 ,...,n} andZn={ 0 }∪Nnfor any n∈N.Let X be a topological space and f:X→X be a continuous map.Forx∈X,O(x,f) ={ fk(x) :k∈ Z+} is called the orbit of x.The set of periodic points,the set of recurrentpoints,the set ofω-limit points for some x∈X and the set of non-wandering points of fare denoted by P(f) ,R(f) ,ω(x,f) andΩ(f) ,respectively(for the definitions see[1 ] ) .Let A X,we use int(A) ,A… 相似文献
11.
J. J. Charatonik 《Periodica Mathematica Hungarica》1985,16(4):219-236
It is proved that Knaster's type continua and solenoids can be considered as inverse limits of arcs and of circles with confluent bonding mappings. Several other classes of bonding mappings, which are relative to confluent ones, also are discussed. 相似文献
12.
13.
Mohammad Reza R. Moghaddam Ali Reza Salemkar Hossein M. Saanye 《Indagationes Mathematicae》2007,18(1):73-82
In this paper we introduce the concept of Baer-invariant of a pair of groups with respect to a variety of groups v. Some inequalities for the Baer-invariant of a pair of finite groups are obtained, when v is considered to be the Schur-Baer variety. We also present a condition for which the order of the Baerinvariant of a pair of finite groups divides the order of the Baer-invariant of their factor groups. Finally, some inequalities for the Schur-multiplier of a pair of finite nilpotent groups and their factor groups are given. 相似文献
14.
Taras Banakh Dušan Repovš Lyubomyr Zdomskyy 《Journal of Pure and Applied Algebra》2008,212(9):2105-2114
In this paper we answer the question of T. Banakh and M. Zarichnyi constructing a copy of the Fréchet-Urysohn fan Sω in a topological group G admitting a functorial embedding [0,1]⊂G. The latter means that each autohomeomorphism of [0,1] extends to a continuous homomorphism of G. This implies that many natural free topological group constructions (e.g. the constructions of the Markov free topological group, free abelian topological group, free totally bounded group, free compact group) applied to a Tychonov space X containing a topological copy of the space Q of rationals give topological groups containing Sω. 相似文献
15.
S.L. Singh S.N. Mishra 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(6):2243-2248
Coincidence and fixed point theorems for single-valued and multi-valued maps generalizing recent results of Suzuki and Kikkawa are obtained. Various applications, including the existence of common solutions of certain functional equations are presented. 相似文献
16.
Tong-Huei Chang Chi-Ming ChenJin-Hsiang Chang 《Nonlinear Analysis: Theory, Methods & Applications》2008
In this work, we first define the 2-KKM mapping and the generalized 2-KKM mapping on a metric space, and then we apply the property of the hyperconvex metric space to get a KKM theorem and a fixed point theorem without a compactness assumption. Next, by using this KKM theorem, we get some variational inequality theorems and minimax inequality theorems. 相似文献
17.
J. Anuradha 《Topology and its Applications》2009,156(18):2942-2948
In this paper, we introduce the notion of proximal pointwise contraction and obtain the existence of a best proximity point on a pair of weakly compact convex subset of a Banach space and generalize a result of [W.A. Kirk, Mappings of generalized contractive type, J. Math. Anal. Appl. 32 (1970) 567-570; W.A. Kirk, H.K. Xu, Asymptotic pointwise contractions, Nonlinear Anal. 69 (2008) 4706-4712]. 相似文献
18.
We prove several facts about cellularity and κ-cellularity of λ-Lindelöf groups generated by their κ-stable subspaces. For example, if a Lindelöf group G is generated by its κ-stable subspace then κ-cellularity (and hence cellularity) of G does not exceed κ. In particular, ω1-cellularity (and hence cellularity) of a Lindelöf group does not exceed ω1 if this group is generated by its ω1-Lindelöf subspace which is a P-space. For any cardinal μ with ω<μ?c a Lindelöf group G is constructed which is separable (and hence has countable cellularity) while ω-cellularity of G is equal to μ. 相似文献
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20.
Cornelia Dru?u 《Topology》2004,43(5):983-1033
We prove that the filling order is quadratic for a large class of solvable groups and asymptotically quadratic for all -rank one lattices in semisimple groups of -rank at least 3. As a byproduct of auxiliary results we give a shorter proof of the theorem on the nondistorsion of horospheres providing also an estimate of a nondistorsion constant. 相似文献