共查询到20条相似文献,搜索用时 0 毫秒
1.
《Journal of Pure and Applied Algebra》2022,226(9):107039
In this paper we identify a class of profinite groups (totally torsion free groups) that includes all separable Galois groups of fields containing an algebraically closed subfield, and demonstrate that it can be realized as an inverse limit of torsion free virtually finitely generated abelian (tfvfga) profinite groups. We show by examples that the condition is quite restrictive. In particular, semidirect products of torsion free abelian groups are rarely totally torsion free. The result is of importance for K-theoretic applications, since descent problems for tfvfga groups are relatively manageable. 相似文献
2.
Dominique Bourn 《Topology and its Applications》2006,153(8):1341-1364
As any category Gp(E) of internal groups in a given category E, the category Gp(Top) of topological groups possesses the strong algebraic property of protomodularity which carries intrinsic notions of normal subobject and of centrality. Here we explicit and investigate these intrinsic notions in the category Gp(Top). We extend these results to any category TopT of topological semi-Abelian algebras. 相似文献
3.
For a class of groupsF, closed under formation of subgroups and products, we call a subgroupA of a groupG F-regular provided there are two homomorphismsf, g: G » F, withF F, so thatA = {x G |f(x) =g(x)}.A is calledF-normal providedA is normal inG andG/A F. For an arbitrary subgroupA ofG, theF-regular (respectively,F-normal) closure ofA inG is the intersection of allF-regular (respectively,F-normal) subgroups ofG containingA. This process gives rise to two well behaved idempotent closure operators.A groupG is calledF-regular (respectively,F-normal) compact provided for every groupH, andF-regular (respectively,F-normal) subgroupA ofG × H, 2(A) is anF-regular (respectively,F-normal) subgroup ofH. This generalizes the well known Kuratowski-Mrówka theorem for topological compactness.In this paper, theF-regular compact andF-normal compact groups are characterized for the classesF consisting of: all torsion-free groups, allR-groups, and all torsion-free abelian groups. In doing so, new classes of groups having nice properties are introduced about which little is known. 相似文献
4.
《Quaestiones Mathematicae》2013,36(5):623-629
AbstractWe present a new admissibility theorem for Galois structures in the sense of G. Janelidze. It applies to relative exact categories satisfying a suitable relative modularity condition, and extends the known admissibility theorem in the theory of generalized central extensions. We also show that our relative modularity condition holds in every relative exact Goursat category. 相似文献
5.
6.
In the context of categorical topology, more precisely that of T-categories (Hofmann, 2007 [8]), we define the notion of T-colimit as a particular colimit in a V-category. A complete and cocomplete V-category in which limits distribute over T-colimits, is to be thought of as the generalisation of a (co-)frame to this categorical level. We explain some ideas on a T-categorical version of “Stone duality”, and show that Cauchy completeness of a T-category is precisely its sobriety. 相似文献
7.
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
8.
A semitopological group (topological group) is a group endowed with a topology for which multiplication is separately continuous (multiplication is jointly continuous and inversion is continuous). In this paper we use topological games to show that many semitopological groups are in fact topological groups. 相似文献
9.
We formulate two open problems related to and, in a sense, suggested by the Reiterman-Tholen characterization of effective descent morphisms of topological spaces. 相似文献
10.
We classify those closed 3-manifolds whose universal covering space naturally admits the structure of a Lie group 相似文献
11.
Let G be a locally compact Abelian group and μ a Haar measure on G. We prove: (a) If G is connected, then the complement of a union of finitely many translates of subgroups of G with infinite index is μ-thick and everywhere of second category. (b) Under a simple (and fairly general) assumption on G, for every cardinal number m such that ℵ0?m?|G| there is a subgroup of G of index m that is μ-thick and everywhere of second category. These results extend theorems by Muthuvel and Erd?s-Marcus, respectively. (b) also implies a recent theorem by Comfort-Raczkowski-Trigos stating that every nondiscrete compact Abelian group G admits 2|G|-many μ-nonmeasurable dense subgroups. 相似文献
12.
George JanelidzeManuela Sobral 《Journal of Pure and Applied Algebra》2002,174(3):303-309
It is known that every effective (global-) descent morphism of topological spaces is an effective étale-descent morphism. On the other hand, in the predecessor of this paper we gave examples of:
- •
- a descent morphism that is not an effective étale-descent morphism;
- •
- an effective étale-descent morphism that is not a descent morphism.
13.
Manuela Sobral 《Applied Categorical Structures》1996,4(1):97-106
The paper deals with (effective) descent morphisms for subfibrations
X of the basic fibration Top/X, for topological spaces X and classes
of continuous functions stable under pullback. For a category with pullbacks, we prove the stability under pullback of effective
-descent morphisms for a class
satisfying some suitable conditions. This plays a rôle in relating effective
-descent to effective global-descent and enables us to obtain a criterion for effective étale-descent. We also show that the inclusion of the class of effective global-descent maps in the class surjective effective étale-descent is strict.Partial financial support by Centro de Matemática da Universidade de Coimbra is gratefully acknowledged. 相似文献
14.
We define for a compactly generated totally disconnected locally compact group a graph, called a rough Cayley graph, that
is a quasi-isometry invariant of the group. This graph carries information about the group structure in an analogous way to
the ordinary Cayley graph for a finitely generated group. With this construction the machinery of geometric group theory can
be applied to topological groups. This is illustrated by a study of groups where the rough Cayley graph has more than one
end and a study of groups where the rough Cayley graph has polynomial growth.
Supported by project J2245 of the Austrian Science Fund (FWF) and be an IEF Marie Curie Fellowship of the Commission of the
European Union. 相似文献
15.
Gábor Lukács 《Journal of Pure and Applied Algebra》2007,208(3):1159-1168
For a compact Hausdorff abelian group K and its subgroup H≤K, one defines the g-closuregK(H) of H in K as the subgroup consisting of χ∈K such that χ(an)?0 in T=R/Z for every sequence {an} in (the Pontryagin dual of K) that converges to 0 in the topology that H induces on . We prove that every countable subgroup of a compact Hausdorff group is g-closed, and thus give a positive answer to two problems of Dikranjan, Milan and Tonolo. We also show that every g-closed subgroup of a compact Hausdorff group is realcompact. The techniques developed in the paper are used to construct a close relative of the closure operator g that coincides with the Gδ-closure on compact Hausdorff abelian groups, and thus captures realcompactness and pseudocompactness of subgroups. 相似文献
16.
Jin-Hwan Cho 《Journal of Pure and Applied Algebra》2003,178(3):245-254
Let H be a closed normal subgroup of a compact Lie group G such that G/H is connected. This paper provides a necessary and sufficient condition for every complex representation of H to be extendible to G, and also for every complex G-vector bundle over the homogeneous space G/H to be trivial. In particular, we show that the condition holds when the fundamental group of G/H is torsion free. 相似文献
17.
Adam J. Prze?dziecki 《Advances in Mathematics》2010,225(4):1893-1913
We construct a functor F:Graphs→Groups which is faithful and “almost” full, in the sense that every nontrivial group homomorphism FX→FY is a composition of an inner automorphism of FY and a homomorphism of the form Ff, for a unique map of graphs f:X→Y. When F is composed with the Eilenberg-Mac Lane space construction K(FX,1) we obtain an embedding of the category of graphs into the unpointed homotopy category which is full up to null-homotopic maps.We provide several applications of this construction to localizations (i.e. idempotent functors); we show that the questions:
- (1)
- Is every orthogonality class reflective?
- (2)
- Is every orthogonality class a small-orthogonality class?
18.
Salvador Hernández 《Mathematische Zeitschrift》2001,238(3):493-503
A topological Abelian group G is Pontryagin reflexive, or P-reflexive for short, if the natural homomorphism of G to its bidual group is a topological isomorphism. We look at the question, set by Kaplan in 1948, of characterizing the topological
Abelian groups that are P-reflexive. Thus, we find some conditions on an arbitrary group G that are equivalent to the P-reflexivity of G and give an example that corrects a wrong statement appearing in previously existent characterizations of P-reflexive groups.
Received: 10 February 2000 / Published online: 17 May 2001 相似文献
19.
L.D. Nel 《Topology and its Applications》1981,12(3):321-330
It is shown that a development of universal topological algebra, based in the obvious way on the category of topological spaces, leads in general to a pathological situation. The pathology disappears when the base category is changed to a cartesian closed topological category or to a topological category endowed with a compatible closed symmetric monoidal structure, provided that in the latter case, the algebraic operations are expressed in terms of monoidal powers rather than the usual cartesian powers. With such base categories, universal topological algebra becomes virtually as well-behaved as ordinary (setbased) universal algebra. 相似文献
20.