Search results for "group theory"
showing 10 items of 703 documents
Irreducible characters of $3'$-degree of finite symmetric, general linear and unitary groups
2018
Abstract Let G be a finite symmetric, general linear, or general unitary group defined over a field of characteristic coprime to 3. We construct a canonical correspondence between irreducible characters of degree coprime to 3 of G and those of N G ( P ) , where P is a Sylow 3-subgroup of G . Since our bijections commute with the action of the absolute Galois group over the rationals, we conclude that fields of values of character correspondents are the same.
ON A QUESTION OF BEIDLEMAN AND ROBINSON
2002
[EN] In [J. C. Beidleman, D. J. S. Robinson, J. Algebra 1997, 191, 686--703, Theorem A], Beidleman and Robinson proved that if a group satisfies the permutizer condition, it is soluble, its chief factors have order a prime number or 4 and G induces the full group of automorphisms in the chief factors of order 4. In this paper, we show that the converse of this theorem is false by showing some counterexamples. We also find some sufficient conditions for a group satisfying the converse of that theorem to satisfy the permutizer condition.
Picard-Fuchs operators for octic arrangements, I: the case of orphans
2019
We report on $25$ families of projective Calabi-Yau threefolds that do not have a point of maximal unipotent monodromy in their moduli space. The construction is based on an analysis of certain pencils of octic arrangements that were found by C. Meyer. There are seven cases where the Picard-Fuchs operator is of order two and $18$ cases where it is of order four. The birational nature of the Picard-Fuchs operator can be used effectively to distinguish between families whose members have the same Hodge numbers.
Finite Groups with Odd Sylow Normalizers
2016
We determine the non-abelian composition factors of the finite groups with Sylow normalizers of odd order. As a consequence, among others, we prove the McKay conjecture and the Alperin weight conjecture for these groups.
Remarks on iteration of formal automorphisms
1988
Etude de l'iteration des automorphismes formels. Generalisation et interpretation d'un critere de Reich-Schwaiger
Strong Converse Results for Linking Operators and Convex Functions
2020
We consider a family B n , ρ c of operators which is a link between classical Baskakov operators (for ρ = ∞ ) and their genuine Durrmeyer type modification (for ρ = 1 ). First, we prove that for fixed n , c and a fixed convex function f , B n , ρ c f is decreasing with respect to ρ . We give two proofs, using various probabilistic considerations. Then, we combine this property with some existing direct and strong converse results for classical operators, in order to get such results for the operators B n , ρ c applied to convex functions.
Malliavin Calculus of Bismut Type for Fractional Powers of Laplacians in Semi-Group Theory
2011
We translate into the language of semi-group theory Bismut's Calculus on boundary processes (Bismut (1983), Lèandre (1989)) which gives regularity result on the heat kernel associated with fractional powers of degenerated Laplacian. We translate into the language of semi-group theory the marriage of Bismut (1983) between the Malliavin Calculus of Bismut type on the underlying diffusion process and the Malliavin Calculus of Bismut type on the subordinator which is a jump process.
Integrability via Reversibility
2017
Abstract A class of left-invariant second order reversible systems with functional parameter is introduced which exhibits the phenomenon of robust integrability: an open and dense subset of the phase space is filled with invariant tori carrying quasi-periodic motions, and this behavior persists under perturbations within the class. Real-analytic volume preserving systems are found in this class which have positive Lyapunov exponents on an open subset, and the complement filled with invariant tori.
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.
Generic properties of singular trajectories
1997
Abstract Let M be a σ-compact C∞ manifold of dimension d ≥ 3. Consider on M a single-input control system : x (t) = F 0 (x(t)) + u(t) F 1 (x(t)) , where F0, F1 are C∞ vector fields on M and the set of admissible controls U is the set of bounded measurable mappings u : [0Tu]↦ R , Tu > 0. A singular trajectory is an output corresponding to a control such that the differential of the input-output mapping is not of maximal rank. In this article we show that for an open dense subset of the set of pairs of vector fields (F0, F1), endowed with the C∞-Whitney topology, all the singular trajectories are with minimal order and the corank of the singularity is one.