Search results for "group theory"
showing 10 items of 703 documents
Degrees of characters in the principal block
2021
Abstract Let G be a finite group. We prove that if the set of degrees of characters in the principal p-block of G has size at most 2 then G is p-solvable, and G / O p ′ ( G ) has a metabelian normal Sylow p-subgroup. The general question of proving that if an arbitrary p-block has two degrees then their defect groups are metabelian remains open.
Binary Patterns in Infinite Binary Words
2002
In this paper we study the set P(w) of binary patterns that can occur in one infinite binary word w, comparing it with the set F(w) of factors of the word. Since the set P(w) can be considered as an extension of the set F(w), we first investigate how large is such extension, by introducing the parameter ?(w) that corresponds to the cardinality of the difference set P(w) \ F(w). Some non trivial results about such parameter are obtained in the case of the Thue-Morse and the Fibonacci words. Since, in most cases, the parameter ?(w) is infinite, we introduce the pattern complexity of w, which corresponds to the complexity of the language P(w). As a main result, we prove that there exist infini…
The set of conjugacy class sizes of a finite group does not determine its solvability
2014
Abstract We find a pair of groups, one solvable and the other non-solvable, with the same set of conjugacy class sizes.
Maximal subgroups and formations
1989
Abstract We define, in each finite group G , some subgroups of Frattini-type in relation with a saturated formation and with a set of primes and study their properties, especially their influence in the structure of G .
On a projective representation of chain geometries
1984
We define a distance d on the set of r-spaces of an n-space. By the transfer of d to the GrasmannianG=G(n, r) we obtain a distinguished class of normal rational curves of order 1, the “1-distance lines’, 1=1,..., r, which are in 1–1-correspondence to the so-called “generalized reguli of type (r, 1)”.
CubeHarmonic: A New Interface from a Magnetic 3D Motion Tracking System to Music Performance
2018
We developed a new musical interface, CubeHarmonic, with the magnetic 3D motion tracking system IM3D. This sys- tem precisely tracks positions of tiny, wireless, battery-less, and identifiable markers (LC coils) in real time. The Cube- Harmonic is a musical application of the Rubik’s cube, with notes on each little piece. Scrambling the cube, we get dif- ferent chords and chord sequences. Positions of the pieces which contain LC coils are detected through IM3D, and transmitted to the computer to recognize the status of the Rubik’s cube, that plays sounds. The central position of the cube is also measured by the LC coils located into the corners of Rubik’s cube, and, depending on the positio…
Abelian antipowers in infinite words
2019
Abstract An abelian antipower of order k (or simply an abelian k-antipower) is a concatenation of k consecutive words of the same length having pairwise distinct Parikh vectors. This definition generalizes to the abelian setting the notion of a k-antipower, as introduced in Fici et al. (2018) [7] , that is a concatenation of k pairwise distinct words of the same length. We aim to study whether a word contains abelian k-antipowers for arbitrarily large k. S. Holub proved that all paperfolding words contain abelian powers of every order (Holub, 2013 [8] ). We show that they also contain abelian antipowers of every order.
Hegel’s Conceptual Group Action on Creative Dynamics in Music
2014
The present paper presents a mechanism to catalyze that crucial step in a creative process, where the critical concept’s “walls” (referring to the common “box” metaphor) are identified and opened. We propose a concrete, but generic body of six concepts and the action of a group of transformations of this body, a toolbox that should offer a set of operational perspectives onto the critical concept’s walls. The conceptual body and the group action are deduced from the first paragraphs of Georg Wilhelm Friedrich Hegel’s Wissenschaft der Logik. On this body, a group, called the “Hegel group”, acts and reflects some of the relations and operations that are hidden in Hegel’s text. We then identif…
Multiple Canard Cycles in Generalized Liénard Equations
2001
AbstractThe paper treats multiple limit cycle bifurcations in singular perturbation problems of planar vector fields. The results deal with any number of parameters. Proofs are based on the techniques introduced in “Canard Cycles and Center Manifolds” (F. Dumortier and R. Roussarie, 1996, Mem. Amer. Math. Soc., 121). The presentation is limited to generalized Liénard equations εx+α(x, c)x+β(x, c)=0.
Spaces of weighted symbols and weighted sobolev spaces on manifolds
1987
This paper gives an approach to pseudodifferential operators on noncompact manifolds using a suitable class of weighted symbols and Sobolev spaces introduced by H.O. Cordes on ℙ. Here, these spaces are shown to be invariant under certain changes of coordinates. It is therefore possible to transfer them to manifolds with a compatible structure.