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1.
By means of the theory of bispaces we show that a countably compact T0 paratopological group (G, τ) is a topological group if and only if (G, τ ∨ τ-1) is ω-bounded (here τ-1 is the conjugate topology of τ). Our approach is premised on the fact that every paratopological countably compact paratopological
group is a Baire space and on the notion of a 2-pseudocompact space. We also prove that every ω-bounded (respectively, topologically
periodic) Baire paratopological group admits a weaker Hausdorff group topology. In particular, ω-bounded (respectively, topologically
periodic) 2-pseudocompact (so, also countably compact) paratopological groups enjoy this property. Some topological properties
turning countably compact topological semigroups into topological groups are presented and some open questions are posed. 相似文献
2.
Let f : U → X be a map from a connected nilpotent space U to a connected rational space X. The evaluation subgroup G
*(U, X; f), which is a generalization of the Gottlieb group of X, is investigated. The key device for the study is an explicit Sullivan model for the connected component containing f of the function space of maps from U to X, which is derived from the general theory of such a model due to Brown and Szczarba (Trans Am Math Soc 349, 4931–4951, 1997).
In particular, we show that non Gottlieb elements are detected by analyzing a Sullivan model for the map f and by looking at non-triviality of higher order Whitehead products in the homotopy group of X. The Gottlieb triviality of a fibration in the sense of Lupton and Smith (The evaluation subgroup of a fibre inclusion, 2006)
is also discussed from the function space model point of view. Moreover, we proceed to consideration of the evaluation subgroup
of the fundamental group of a nilpotent space. In consequence, the first Gottlieb group of the total space of each S
1-bundle over the n-dimensional torus is determined explicitly in the non-rational case.
相似文献
3.
Francesco de Giovanni Alessio Russo Giovanni Vincenzi 《Mediterranean Journal of Mathematics》2007,4(1):65-71
A subgroup X of a group G is called pronormal-by-finite if there exists a pronormal subgroup Y of G such that Y ≤ X and |X : Y| is finite. The structure of (generalized) soluble groups in which all subgroups are pronormal-by-finite is investigated.
Among other results, it is proved in particular that a finitely generated soluble group with such property is central-by-finite,
provided that it has no infinite dihedral sections. 相似文献
4.
Leonid A. Kurdachenko Javier Otal Alessio Russo Giovanni Vincenzi 《Central European Journal of Mathematics》2011,9(2):420-432
This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We characterize the structure of such G in case they are locally finite. If G is a hyperabelian group and has the property, we show that every subgroup of G is in fact ascendant provided G is locally nilpotent or non-periodic. We also restrict our study replacing ascendant subgroups by permutable subgroups, which
of course are ascendant [Stonehewer S.E., Permutable subgroups of infinite groups, Math. Z., 1972, 125(1), 1–16]. 相似文献
5.
Let n ≥ 0, let ω be a nonempty set of prime numbers and let τ be a subgroup functor (in Skiba’s sense) such that all subgroups
of any finite group G contained in τ (G) are subnormal in G. It is shown that the lattice of all τ-closed n-multiply ω-composite formations is algebraic and modular. 相似文献
6.
Yildiray Ozan 《Geometriae Dedicata》2004,108(1):131-140
Let X
0 be a topological component of a nonsingular real algebraic variety and i:X → X
C
is a nonsingular projective complexification of X. In this paper, we will study the homomorphism on homotopy groups induced by the inclusion map i:X
0 → X
C
and obtain several results using rational homotopy theory and other standard tools of homotopy theory. 相似文献
7.
Shi Rong LI 《数学学报(英文版)》2005,21(4):797-802
For a finite group G, let T(G) denote a set of primes such that a prime p belongs to T(G) if and only if p is a divisor of the index of some maximal subgroup of G. It is proved that if G satisfies any one of the following conditions: (1) G has a p-complement for each p∈T(G); (2)│T(G)│= 2: (3) the normalizer of a Sylow p-subgroup of G has prime power index for each odd prime p∈T(G); then G either is solvable or G/Sol(G)≌PSL(2, 7) where Sol(G) is the largest solvable normal subgroup of G. 相似文献
8.
Manley Perkel 《Israel Journal of Mathematics》1985,52(1-2):167-176
For integersa, b andc, the groupF
a,b,−c is defined to be the group 〈R, S : R
2=RS
aRSbRS−c=1〉. In this paper we identify certain subgroups of the group of affine linear transformations of finite fields of orderp
n (for certainp andn) as groups of typeF
a,b,−c for certain (not unique) choices ofa, b andc. 相似文献
9.
Li Fang WANG Yan Ming WANG 《数学学报(英文版)》2007,23(11):1985-1990
Let З be a complete set of Sylow subgroups of a finite group G, that is, З contains exactly one and only one Sylow p-subgroup of G for each prime p. A subgroup of a finite group G is said to be З-permutable if it permutes with every member of З. Recently, using the Classification of Finite Simple Groups, Heliel, Li and Li proved tile following result:
If the cyclic subgroups of prime order or order 4 iif p = 2) of every member of З are З-permutable subgroups in G, then G is supersolvable.
In this paper, we give an elementary proof of this theorem and generalize it in terms of formation. 相似文献
10.
Christopher L. Douglas 《K-Theory》2005,36(1-2):59-82
We prove that the composition of the A-theory transfer with the trace map to stable homotopy is weakly homotopic to the Becker–Gottlieb
transfer. This shows that the Waldhausen splitting A(*) ≃ Q (S0) × Wh(*) of A-theory into stable homotopy and the Whitehead space is natural with respect to transfer maps.
(Received: September 2003)
Christopher L. Douglas - The author was partially supported by a scholarship from the Rhodes Trust. 相似文献
11.
Subgroups of Word Hyperbolic Groups in Dimension 2 总被引:1,自引:0,他引:1
If G is a word hyperbolic group of cohomological dimension 2,then every subgroup of G of type FP2 is also word hyperbolic.Isoperimetric inequalities are defined for groups of type FP2and it is shown that the linear isoperimetric inequality inthis generalized context is equivalent to word hyperbolicity.A sufficient condition for hyperbolicity of a general graphis given along with an application to relative hyperbolicity.Finitely presented subgroups of Lyndon's small cancellationgroups of hyperbolic type are word hyperbolic. Finitely presentedsubgroups of hyperbolic 1-relator groups are hyperbolic. Finitelypresented subgroups of free Burnside groups are finite in thestable range. 相似文献
12.
A group G satisfies the weak maximality condition for nonnilpotent subgroups [or, briefly, the Wmax-(nonnil) condition if G does not have infinite increasing chains {H
n
| n ∈ ℕ} of nonnilpotent subgroups such that the indices |H
n+1: H
n
| are infinite for each n ∈ ℕ. We study the structure of hypercentral groups satisfying the weak maximality condition for nonnilpotent subgroups.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 8, pp. 1068–1083, August, 2006. 相似文献
13.
Let G be a noncompact semi-simple Lie group and a Lie semigroup with nonempty interior. We study the homotopy groups , , of S. Generalizing a well known fact for G, it is proved that there exists a compact and connected subgroup such that is isomorphic to . Furthermore, there exists a coset z contained in int S which is a deformation retract of S. 相似文献
14.
Ehud Meir 《Algebras and Representation Theory》2012,15(2):391-405
We define a notion of complexity for modules over group rings of infinite groups. This generalizes the notion of complexity
for modules over group algebras of finite groups. We show that if M is a module over the group ring kG, where k is any ring and G is any group, and M has f-complexity (where f is some complexity function) over some set of finite index subgroups of G, then M has f-complexity over G (up to a direct summand). This generalizes the Alperin-Evens Theorem, which states that if the group G is finite then the complexity of M over G is the maximal complexity of M over an elementary abelian subgroup of G. We also show how we can use this generalization in order to construct projective resolutions for the integral special linear
groups, SL(n, ℤ), where n ≥ 2. 相似文献
15.
ABSTRACT Some properties of abnormal and pronormal subgroups in generalized minimax groups are considered. For generalized minimax groups (not only periodic) whose locally nilpotent residual is nilpotent and satisfies Min-G the existence of Carter subgroups and their conjugations have been proven. Some generalizations of results of J. Rose on abnormal and contranormal subgroups have been also obtained. 相似文献
16.
Let n, k, τ, d be positive integers with 1 ≤ k, τ, d ≤ n. As natural extensions of the bases, the kth local bases, the kth upper bases and the kth lower bases of primitive non-powerful signed digraphs, we introduce a number of new, though, intimately related parameters
called the generalized τ-bases of primitive non-powerful signed digraphs. Moreover, some sharp bounds for the generalized τ-bases of primitive non-powerful signed digraphs with n vertices and d loops are obtained, respectively. 相似文献
17.
Let G be a finite group and H a subgroup of G. We say that: (1) H is τ-quasinormal in G if H permutes with all Sylow subgroups Q of G such that (|Q|, |H|) = 1 and (|H|, |Q
G
|) ≠ 1; (2) H is weakly τ-quasinormal in G if G has a subnormal subgroup T such that HT = G and T ∩ H ≦ H
τG
, where H
τG
is the subgroup generated by all those subgroups of H which are τ-quasinormal in G. Our main result here is the following. Let ℱ be a saturated formation containing all supersoluble groups and let X ≦ E be normal subgroups of a group G such that G/E ∈ ℱ. Suppose that every non-cyclic Sylow subgroup P of X has a subgroup D such that 1 < |D| < |P| and every subgroup H of P with order |H| = |D| and every cyclic subgroup of P with order 4 (if |D| = 2 and P is non-Abelian) not having a supersoluble supplement in G is weakly τ-quasinormal in G. If X is either E or F* (E), then G ∈ ℱ. 相似文献
18.
This paper presents adaptive algorithms for eigenvalue problems associated with non-selfadjoint partial differential operators.
The basis for the developed algorithms is a homotopy method which departs from a well-understood selfadjoint problem. Apart
from the adaptive grid refinement, the progress of the homotopy as well as the solution of the iterative method are adapted
to balance the contributions of the different error sources. The first algorithm balances the homotopy, discretization and
approximation errors with respect to a fixed stepsize τ in the homotopy. The second algorithm combines the adaptive stepsize control for the homotopy with an adaptation in space
that ensures an error below a fixed tolerance ε. The outcome of the analysis leads to the third algorithm which allows the complete adaptivity in space, homotopy stepsize
as well as the iterative algebraic eigenvalue solver. All three algorithms are compared in numerical examples. 相似文献
19.
Let G be a noncompact semi-simple Lie group and a Lie semigroup with nonempty interior. We study the homotopy groups , , of S. Generalizing a well known fact for G, it is proved that there exists a compact and connected subgroup such that is isomorphic to . Furthermore, there exists a coset
z contained in int S which is a deformation retract of S.
Received 6 December 2000; in revised form 23 November 2001 相似文献
20.
Anthony M. Bloch Peter E. Crouch Jerrold E. Marsden Amit K. Sanyal 《Foundations of Computational Mathematics》2008,8(4):469-500
The purpose of this paper is to extend the symmetric representation of the rigid body equations from the group SO (n) to other groups. These groups are matrix subgroups of the general linear group that are defined by a quadratic matrix identity.
Their corresponding Lie algebras include several classical semisimple matrix Lie algebras. The approach is to start with an
optimal control problem on these groups that generates geodesics for a left-invariant metric. Earlier work by Bloch, Crouch,
Marsden, and Ratiu defines the symmetric representation of the rigid body equations, which is obtained by solving the same
optimal control problem in the particular case of the Lie group SO (n). This paper generalizes this symmetric representation to a wider class of matrix groups satisfying a certain quadratic matrix
identity. We consider the relationship between this symmetric representation of the generalized rigid body equations and the
generalized rigid body equations themselves. A discretization of this symmetric representation is constructed making use of
the symmetry, which in turn give rise to numerical algorithms to integrate the generalized rigid body equations for the given
class of matrix Lie groups.
Dedicated to Professor Arieh Iserles on the Occasion of his Sixtieth Birthday. 相似文献