Search results for "permuta"
showing 10 items of 171 documents
Abelian Gradings on Upper Block Triangular Matrices
2012
AbstractLet G be an arbitrary finite abelian group. We describe all possible G-gradings on upper block triangular matrix algebras over an algebraically closed field of characteristic zero.
On finite minimal non-nilpotent groups
2005
[EN] A critical group for a class of groups X is a minimal non-X-group. The critical groups are determined for various classes of finite groups. As a consequence, a classification of the minimal non-nilpotent groups (also called Schmidt groups) is given, together with a complete proof of Gol¿fand¿s theorem on maximal Schmidt groups.
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.
A generalization to Sylow permutability of pronormal subgroups of finite groups
2020
[EN] In this note, we present a new subgroup embedding property that can be considered as an analogue of pronormality in the scope of permutability and Sylow permutability in finite groups. We prove that finite PST-groups, or groups in which Sylow permutability is a transitive relation, can be characterized in terms of this property, in a similar way as T-groups, or groups in which normality is transitive, can be characterized in terms of pronormality.
Qualitative analysis of matrix splitting methods
2001
Abstract Qualitative properties of matrix splitting methods for linear systems with tridiagonal and block tridiagonal Stieltjes-Toeplitz matrices are studied. Two particular splittings, the so-called symmetric tridiagonal splittings and the bidiagonal splittings, are considered, and conditions for qualitative properties like nonnegativity and shape preservation are shown for them. Special attention is paid to their close relation to the well-known splitting techniques like regular and weak regular splitting methods. Extensions to block tridiagonal matrices are given, and their relation to algebraic representations of domain decomposition methods is discussed. The paper is concluded with ill…
Diagonalization of indefinite saddle point forms
2020
We obtain sufficient conditions that ensure block diagonalization (by a direct rotation) of sign-indefinite symmetric sesquilinear forms as well as the associated operators that are semi-bounded neither from below nor from above. In the semi-bounded case, we refine the obtained results and, as an example, revisit the block Stokes operator from fluid dynamics.
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.
CubeHarmonic: A new musical instrument based on Rubik{'}s cube with embedded motion sensor
2019
A contemporary challenge involves scientific education and the connection between new technologies and the heritage of the past. CubeHarmonic (CH) joins novelty and tradition, creativity and edu- cation, science and art. It takes shape as a novel musical instrument where magnetic 3D motion tracking technology meets musical per- formance and composition. CH is a Rubik’s cube with a note on each facet, and a chord or chord sequence on each face. The posi- tion of each facet is detected through magnetic 3D motion tracking. While scrambling the cube, the performer gets new chords and new chord sequences. CH can be used to compose, improvise,1 and teach music and mathematics (group theory, permu…
Hypercube + Rubik’s Cube + Music = HyperCubeHarmonic
2022
Musical chords and chord relations can be described through mathematics. Abstract permutations can be visualized through the Rubik’s cube, born as a pedagogical device [7,21]. Permutations of notes can also be heard through the CubeHarmonic, a novel musical instru- ment. Here, we summarize the basic ideas and the state of the art of the physical implementation of CubeHarmonic, discussing its conceptual lift- ing up to the fourth dimension, with the HyperCubeHarmonic (HCH). We present the basics of the hypercube theory and of the 4-dimensional Rubik’s cube, investigating its potential for musical applications. To gain intuition about HCH complexity, we present two practical implementa- tions…
I vincoli della trasformazione: riflessioni sulla metamorfosi tra letteratura, filosofia e biologia
2019
Per sopravvivere gli esseri viventi sono costretto a modificarsi di continuo, adattandosi all’ambiente e al variare delle circostanze. In questa costante alterazione formale come si conciliano identità e mutamento? Come può l’individuo preservarsi dal totale dissolvimento in qualcos’altro? Questi sono solo alcuni dei quesiti che nei secoli hanno spinto studiosi di Morfologia, Estetica e Biologia a indagare le trasformazioni organiche. Nella presente trattazione cercheremo di chiarire le somiglianze e le differenze fra alcuni concetti chiave del vocabolario della metamorfosi (trasformazione, permutazione, vincolo, libertà di cambiamento, modularità organica) adottando un approccio multidisci…