Search results for "Group Theory"
showing 10 items of 703 documents
Maximal subgroups of small index of finite almost simple groups
2022
We prove in this paper that a finite almost simple group $R$ with socle the non-abelian simple group $S$ possesses a conjugacy class of core-free maximal subgroups whose index coincides with the smallest index $\operatorname{l}(S)$ of a maximal group of $S$ or a conjugacy class of core-free maximal subgroups with a fixed index $v_S \leq {\operatorname{l}(S)^2}$, depending only on $S$. We show that the number of subgroups of the outer automorphism group of $S$ is bounded by $\log^3 {\operatorname{l}(S)}$ and $\operatorname{l}(S)^2 < |S|$.
Rational solutions to the KPI equation from particular polynomials
2022
Abstract We construct solutions to the Kadomtsev–Petviashvili equation (KPI) from particular polynomials. We obtain rational solutions written as a second spatial derivative of a logarithm of a determinant of order n . We obtain with this method an infinite hierarchy of rational solutions to the KPI equation. We give explicitly the expressions of these solutions for the first five orders.
Méthodes géométriques et analytiques pour étudier l'application exponentielle, la sphère et le front d'onde en géométrie sous-riemannienne dans le ca…
1999
Consider a sub-riemannian geometry (U,D,g) where U is a neighborhood of 0 in R 3 , D is a Martinet type distribution identified to ker ω , ω being the 1-form: , q=(x,y,z) and g is a metric on D which can be taken in the normal form : , a=1+yF(q) , c=1+G(q) , . In a previous article we analyze the flat case : a=c=1 ; we describe the conjugate and cut loci , the sphere and the wave front . The objectif of this article is to provide a geometric and computational framework to analyze the general case. This frame is obtained by analysing three one parameter deformations of the flat case which clarify the role of the three parameters in the gradated normal form of order 0 where: , . More generall…
Gray visiting Motzkins
2002
We present the first Gray code for Motzkin words and their generalizations: k colored Motzkin words and Schroder words. The construction of these Gray codes is based on the observation that a k colored Motzkin word is the shuffle of a Dyck word by a k-ary variation on a trajectory which is a combination. In the final part of the paper we give some algorithmic considerations and other possible applications of the techniques introduced here.
Rational irreducible characters and rational conjugacy classes in finite groups
2007
We prove that a finite group G G has two rational-valued irreducible characters if and only if it has two rational conjugacy classes, and determine the structure of any such group. Along the way we also prove a conjecture of Gow stating that any finite group of even order has a non-trivial rational-valued irreducible character of odd degree.
Some subgroup embeddings in finite groups: A mini review
2015
[EN] In this survey paper several subgroup embedding properties related to some types of permutability are introduced and studied. ª 2014 Production and hosting by Elsevier B.V. on behalf of Cairo University
Method for determining the proper expansion center and order for Mellin radial harmonic filters
1993
Abstract A method to improve the behaviour of the Mellin radial harmonic (MRH) filters in scale invariant pattern recognition is presented. An algorithm has been introduced to obtain the proper expansion center and order of the MRH development of any object. The procedure consists of the suspression of the non-discriminant uniform background in the energy function of the target. Computer simulations are presented.
Commensurability classification of a family of right-angled Coxeter groups
2008
We classify the members of an infinite family of right-angled Coxeter groups up to abstract commensurability.
Glass transitions and scaling laws within an alternative mode-coupling theory
2015
Idealized glass transitions are discussed within an alternative mode-coupling theory (TMCT) proposed by Tokuyama [Physica A 395, 31 (2014)]. This is done in order to identify common ground with and differences from the conventional mode-coupling theory (MCT). It is proven that both theories imply the same scaling laws for the transition dynamics, which are characterized by two power-law decay functions and two diverging power-law time scales. However, the values for the corresponding anomalous exponents calculated within both theories differ from each other. It is proven that the TMCT, contrary to the MCT, does not describe transitions with continuously vanishing arrested parts of the corre…
2-Groups with few rational conjugacy classes
2011
Abstract In this paper we prove the following conjecture of G. Navarro: if G is a finite 2-group with exactly 5 rational conjugacy classes, then G is dihedral, semidihedral or generalized quaternion. We also characterize the 2-groups with 4 rational classes.