Search results for "combinatoric"
showing 10 items of 1776 documents
A note on Sylow permutable subgroups of infinite groups
2014
Abstract A subgroup A of a periodic group G is said to be Sylow permutable, or S-permutable, subgroup of G if A P = P A for all Sylow subgroups P of G. The aim of this paper is to establish the local nilpotency of the section A G / Core G ( A ) for an S-permutable subgroup A of a locally finite group G.
On some classes of supersoluble groups
2007
[EN] Finite groups G for which for every subgroup H and for all primes q dividing the index |G:H| there exists a subgroup K of G such that H is contained in K and |K:H|=q are called Y-groups. Groups in which subnormal subgroups permute with all Sylow subgroups are called PST-groups. In this paper a local version of the Y-property leading to a local characterisation of Y-groups, from which the classical characterisation emerges, is introduced. The relationship between PST-groups and Y-groups is also analysed.
Finite groups with all minimal subgroups solitary
2016
We give a complete classification of the finite groups with a unique subgroup of order p for each prime p dividing its order. All the groups considered in this paper will be finite. One of the most fruitful lines in the research in abstract group theory during the last years has been the study of groups in which the members of a certain family of subgroups satisfy a certain subgroup embedding property. The family of the subgroups of prime order (also called minimal subgroups) has attracted the interest of many mathematicians. For example, a well-known result of Itˆo (see [8, Kapitel III, Satz 5.3; 9]) states that a group of odd order with all minimal subgroups in the center is nilpotent. Th…
On the Frattini subgroup of a finite group
2016
We study the class of finite groups $G$ satisfying $\Phi (G/N)= \Phi(G)N/N$ for all normal subgroups $N$ of $G$. As a consequence of our main results we extend and amplify a theorem of Doerk concerning this class from the soluble universe to all finite groups and answer in the affirmative a long-standing question of Christensen whether the class of finite groups which possess complements for each of their normal subgroups is subnormally closed.
Variational parabolic capacity
2015
We establish a variational parabolic capacity in a context of degenerate parabolic equations of $p$-Laplace type, and show that this capacity is equivalent to the nonlinear parabolic capacity. As an application, we estimate the capacities of several explicit sets.
Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces
2011
The purpose of this paper is to present some fixed point theorems for T -weakly isotone increasing mappings which satisfy a generalized nonlinear contractive condition in complete ordered metric spaces. As application, we establish an existence theorem for a solution of some integral equations.
WEB 2.0 ET MUSÉES Les nouveaux visages du visiteur
2012
WEB 2.0AND MUSEUMS: THE NEW EACES OF THE VISITOR The increasing integration of techniques from Web 2.0 by the museums illustrates the profound changes that these structures have realized in building their relationship with the audience. The use of these devices, based on a logic of participation, leads to involve the visitor, traditionally rather kept at a distance, on all stages of the implemeritation of the mUseum offered on Internet. Through a careful examinât icin of sites arid features offered by the museal structures, different roles now devolved to the public have been identified. The emergence of these new "faces" of the visitor comes to question, in the longer-term, about the ident…
A Complete, Exact and Efficient Implementation for Computing the Edge-Adjacency Graph of an Arrangement of Quadrics
2011
International audience; We present a complete, exact and efficient implementation to compute the edge-adjacency graph of an arrangement of quadrics, i.e. surfaces of algebraic degree 2. This is a major step towards the computation of the full 3D arrangement. We enhanced an implementation for an exact parameterization of the intersection curves of two quadrics, such that we can compute the exact parameter value for intersection points and from that the edge-adjacency graph of the arrangement. Our implementation is complete in the sense that it can handle all kinds of inputs including all degenerate ones, i.e. singularities or tangential intersection points. It is exact in that it always comp…
On Prefix Normal Words
2011
We present a new class of binary words: the prefix normal words. They are defined by the property that for any given length $k$, no factor of length $k$ has more $a$'s than the prefix of the same length. These words arise in the context of indexing for jumbled pattern matching (a.k.a. permutation matching or Parikh vector matching), where the aim is to decide whether a string has a factor with a given multiplicity of characters, i.e., with a given Parikh vector. Using prefix normal words, we give the first non-trivial characterization of binary words having the same set of Parikh vectors of factors. We prove that the language of prefix normal words is not context-free and is strictly contai…
Permutations of zero-sumsets in a finite vector space
2020
Abstract In this paper, we consider a finite-dimensional vector space 𝒫 {{\mathcal{P}}} over the Galois field GF ( p ) {\operatorname{GF}(p)} , with p being an odd prime, and the family ℬ k x {{\mathcal{B}}_{k}^{x}} of all k-sets of elements of 𝒫 {\mathcal{P}} summing up to a given element x. The main result of the paper is the characterization, for x = 0 {x=0} , of the permutations of 𝒫 {\mathcal{P}} inducing permutations of ℬ k 0 {{\mathcal{B}}_{k}^{0}} as the invertible linear mappings of the vector space 𝒫 {\mathcal{P}} if p does not divide k, and as the invertible affinities of the affine space 𝒫 {\mathcal{P}} if p divides k. The same question is answered also in the case where …