Search results for "Number"
showing 10 items of 3939 documents
A reduction theorem for a conjecture on products of two π -decomposable groups
2013
[EN] For a set of primes pi, a group X is said to be pi-decomposable if X = X-pi x X-pi' is the direct product of a pi-subgroup X-pi and a pi'-subgroup X-pi', where pi' is the complementary of pi in the set of all prime numbers. The main result of this paper is a reduction theorem for the following conjecture: "Let pi be a set of odd primes. If the finite group G = AB is a product of two pi-decomposable subgroups A = A(pi) x A(pi') and B = B-pi x B-pi', then A(pi)B(pi) = B(pi)A(pi) and this is a Hall pi-subgroup of G." We establish that a minimal counterexample to this conjecture is an almost simple group. The conjecture is then achieved in a forthcoming paper. (C) 2013 Elsevier Inc. All ri…
On self-normalising subgroups of finite groups
2010
[EN] The aim of this paper is to characterise the classes of groups in which every subnormal subgroup is normal, permutable, or S-permutable by the embedding of the subgroups (respectively, subgroups of prime power order) in their normal, permutable, or S-permutable closure, respectively.
On the orders of zeros of irreducible characters
2009
Let G be a finite group and p a prime number. We say that an element g in G is a vanishing element of G if there exists an irreducible character χ of G such that χ (g) = 0. The main result of this paper shows that, if G does not have any vanishing element of p-power order, then G has a normal Sylow p-subgroup. Also, we prove that this result is a generalization of some classical theorems in Character Theory of finite groups. © 2008 Elsevier Inc. All rights reserved.
A Graph Based Algorithm For Intersection Of Subdivision Surfaces
2003
Computing surface intersections is a fundamental problem in geometric modeling. Any boolean operation can be seen as an intersection calculation followed by a selection of the parts necessary for building the surface of the resulting object. A robust and efficient algorithm to compute intersection on subdivision surfaces (surfaces generated by the Loop scheme) is proposed here. This algorithm relies on the concept of a bipartite graph which allows the reduction of the number of faces intersection tests. Intersection computations are accelerated by the use of the bipartite graph and the neighborhood of intersecting faces at a given level of subdivision to deduce intersecting faces at the fol…
Fuzzy functions: a fuzzy extension of the category SET and some related categories
2000
<p>In research Works where fuzzy sets are used, mostly certain usual functions are taken as morphisms. On the other hand, the aim of this paper is to fuzzify the concept of a function itself. Namely, a certain class of L-relations F : X x Y -&gt; L is distinguished which could be considered as fuzzy functions from an L-valued set (X,Ex) to an L-valued set (Y,Ey). We study basic properties of these functions, consider some properties of the corresponding category of L-valued sets and fuzzy functions as well as briefly describe some categories related to algebra and topology with fuzzy functions in the role of morphisms.</p>
On a Category of Extensional Fuzzy Rough Approximation L-valued Spaces
2016
We establish extensionality of some upper and lower fuzzy rough approximation operators on an L-valued set. Taking as the ground basic properties of these operators, we introduce the concept of an (extensional) fuzzy rough approximation L-valued space. We apply fuzzy functions satisfying certain continuity-type conditions, as morphisms between such spaces, and in the result obtain a category \(\mathcal{FRA}{} \mathbf{SPA}(L)\) of fuzzy rough approximation L-valued spaces. An interpretation of fuzzy rough approximation L-valued spaces as L-fuzzy (di)topological spaces is presented and applied for constructing examples in category \(\mathcal{FRA}{} \mathbf{SPA}(L)\).
Machine-Independent Characterizations and Complete Problems for Deterministic Linear Time
2002
This article presents two algebraic characterizations and two related complete problems for the complexity class DLIN that was introduced in [E. Grandjean, Ann. Math. Artif. Intell., 16 (1996), pp. 183--236]. DLIN is essentially the class of all functions that can be computed in linear time on a Random Access Machine which uses only numbers of linear value during its computations. The algebraic characterizations are in terms of recursion schemes that define unary functions. One of these schemes defines several functions simultaneously, while the other one defines only one function. From the algebraic characterizations, we derive two complete problems for DLIN under new, very strict, and mac…
On set-valued cone absolutely summing maps
2009
Spaces of cone absolutely summing maps are generalizations of Bochner spaces Lp(μ, Y), where (Ω, Σ, μ) is some measure space, 1 ≤ p ≤ ∞ and Y is a Banach space. The Hiai-Umegaki space \( \mathcal{L}^1 \left[ {\sum ,cbf(X)} \right] \) of integrably bounded functions F: Ω → cbf(X), where the latter denotes the set of all convex bounded closed subsets of a separable Banach space X, is a set-valued analogue of L1(μ, X). The aim of this work is to introduce set-valued cone absolutely summing maps as a generalization of \( \mathcal{L}^1 \left[ {\sum ,cbf(X)} \right] \) , and to derive necessary and sufficient conditions for a set-valued map to be such a set-valued cone absolutely summing map. We …
Generating restricted classes of involutions, Bell and Stirling permutations
2010
AbstractWe present a recursive generating algorithm for unrestricted permutations which is based on both the decomposition of a permutation as a product of transpositions and that as a union of disjoint cycles. It generates permutations at each recursive step and slight modifications of it produce generating algorithms for Bell permutations and involutions. Further refinements yield algorithms for these classes of permutations subject to additional restrictions: a given number of cycles or/and fixed points. We obtain, as particular cases, generating algorithms for permutations counted by the Stirling numbers of the first and second kind, even permutations, fixed-point-free involutions and d…
Graded algebras with polynomial growth of their codimensions
2015
Abstract Let A be an algebra over a field of characteristic 0 and assume A is graded by a finite group G . We study combinatorial and asymptotic properties of the G -graded polynomial identities of A provided A is of polynomial growth of the sequence of its graded codimensions. Roughly speaking this means that the ideal of graded identities is “very large”. We relate the polynomial growth of the codimensions to the module structure of the multilinear elements in the relatively free G -graded algebra in the variety generated by A . We describe the irreducible modules that can appear in the decomposition, we show that their multiplicities are eventually constant depending on the shape obtaine…