Search results for "Valence"

A note on maximal subgroups and conjugacy classes of finite groups

2021

Given a finite group G, two elements are ≡m-related if they lie in exactly the same maximal subgroups of G. This equivalence relation was introduced by P. J. Cameron, A. Lucchini and C. M. Roney-Do...

Common fixed points in cone metric spaces

2007

In this paper we consider a notion of g-weak contractive mappings in the setting of cone metric spaces and we give results of common fixed points. This results generalize some common fixed points results in metric spaces and some of the results of Huang and Zhang in cone metric spaces.

Formations of Monoids, Congruences, and Formal Languages

2015

The main goal in this paper is to use a dual equivalence in automata theory started in [25] and developed in [3] to prove a general version of the Eilenberg-type theorem presented in [4]. Our principal results confirm the existence of a bijective correspondence between three concepts; formations of monoids, formations of languages and formations of congruences. The result does not require finiteness on monoids, nor regularity on languages nor finite index conditions on congruences. We relate our work to other results in the field and we include applications to non-r-disjunctive languages, Reiterman s equational description of pseudovarieties and varieties of monoids.

On the blockwise modular isomorphism problem

2017

As a generalization of the modular isomorphism problem we study the behavior of defect groups under Morita equivalence of blocks of finite groups over algebraically closed fields of positive characteristic. We prove that the Morita equivalence class of a block B of defect at most 3 determines the defect groups of B up to isomorphism. In characteristic 0 we prove similar results for metacyclic defect groups and 2-blocks of defect 4. In the second part of the paper we investigate the situation for p-solvable groups G. Among other results we show that the group algebra of G itself determines if G has abelian Sylow p-subgroups.

Harnack and Shmul'yan pre-order relations for Hilbert space contractions

2015

We study the behavior of some classes of Hilbert space contractions with respect to Harnack and Shmul'yan pre-orders and the corresponding equivalence relations. We give some conditions under which the Harnack equivalence of two given contractions is equivalent to their Shmul'yan equivalence and to the existence of an arc joining the two contractions in the class of operator-valued contractive analytic functions on the unit disc. We apply some of these results to quasi-isometries and quasi-normal contractions, as well as to partial isometries for which we show that their Harnack and Shmul'yan parts coincide. We also discuss an extension, recently considered by S.~ter~Horst [\emph{J. Operato…

A criterion for homeomorphism between closed Haken manifolds

2003

In this paper we consider two connected closed Haken manifolds denoted by M^3 and N^3, with the same Gromov simplicial volume. We give a simple homological criterion to decide when a given map f: M^3-->N^3 between M^3 and N^3 can be changed by a homotopy to a homeomorphism. We then give a convenient process for constructing maps between M^3 and N^3 satisfying the homological hypothesis of the map f.

From metric spaces to partial metric spaces

2013

Motivated by experience from computer science, Matthews (1994) introduced a nonzero self-distance called a partial metric. He also extended the Banach contraction principle to the setting of partial metric spaces. In this paper, we show that fixed point theorems on partial metric spaces (including the Matthews fixed point theorem) can be deduced from fixed point theorems on metric spaces. New fixed point theorems on metric spaces are established and analogous results on partial metric spaces are deduced. MSC:47H10, 54H25.

Caractérisation des flots d' Anosov en dimension 3 par leurs feuilletages faibles

1995

AbstractWe consider Anosov flows on closed 3-manifolds. We show that if such a flow admits a weak foliation whose lifting in the universal covering is a product foliation, thenit is characterized up to topological equivalence by its weak stable foliation up to topological conjugacy. As a corollary we obtain that, up to topological equivalence and finite coverings, suspensions and geodesic flows are the unique Anosov flows on closed 3-manifolds whose weak stable foliations are transversely projective.

Bilateral denseness of the hyperbolic limit points of groups acting on metric spaces

1997

A group analysis via weak equivalence transformations for a model of tumor encapsulation

2004

A symmetry reduction of a PDEs system, describing the expansive growth of a benign tumour, is obtained via a group analysis approach. The presence in the model of three arbitrary functions suggests the use of Lie symmetries by using the weak equivalence transformations. An invariant classification is given which allows us to reduce the initial PDEs system to an ODEs system. Numerical simulations show a realistic enough description of the physical process.