Search results for " mathematical physics"

On the focal subgroup of a saturated fusion system

2016

Abstract The influence of the cyclic subgroups of order p or 4 of the focal subgroup of a saturated fusion system F over a p -group S is investigated in this paper. Some criteria for normality of S in F as well as necessary and sufficient conditions for nilpotency of F are given. The resistance of a p -group in which every cyclic subgroup of order p or 4 is normal, and earlier results about p -nilpotence of finite groups and nilpotency of saturated fusion systems are consequences of our study.

Landau's theorem and the number of conjugacy classes of zeros of characters

2021

Abstract Motivated by a 2004 conjecture by the author and J. Sangroniz, Y. Yang has recently proved that if G is solvable then the index in G of the 8th term of the ascending Fitting series is bounded in terms of the largest number of zeros in a row in the character table of G. In this note, we prove this result for arbitrary finite groups and propose a stronger form of the 2004 conjecture. We conclude the paper showing some possible ways to prove this strengthened conjecture.

Varieties with at most cubic growth

2019

Abstract Let V be a variety of non necessarily associative algebras over a field of characteristic zero. The growth of V is determined by the asymptotic behavior of the sequence of codimensions c n ( V ) , n = 1 , 2 , … , and here we study varieties of polynomial growth. We classify all possible growth of varieties V of algebras satisfying the identity x ( y z ) ≡ 0 such that c n ( V ) C n α , with 1 ≤ α 3 , for some constant C. We prove that if 1 ≤ α 2 then c n ( V ) ≤ C 1 n , and if 2 ≤ α 3 , then c n ( V ) ≤ C 2 n 2 , for some constants C 1 , C 2 .

The enveloping algebra of the Lie superalgebra osp(1,2)

1990

International audience

2-Brauer correspondent blocks with one simple module

2017

Abstract One of the main problems in representation theory is to understand the exact relationship between Brauer corresponding blocks of finite groups. The case where the local correspondent has a unique simple module seems key. We study this situation for 2-blocks.

Local functions on finite groups

2020

We study local properties of finite groups using chains of p p -subgroups.

Volume growth and parabolicity

2001

Mappings of finite distortion : size of the branch set

2018

Abstract We study the branch set of a mapping between subsets of ℝ n {\mathbb{R}^{n}} , i.e., the set where a given mapping is not defining a local homeomorphism. We construct several sharp examples showing that the branch set or its image can have positive measure.

TANGENTIAL DEFORMATIONS ON FIBRED POISSON MANIFOLDS

2005

In a recent article, Cattaneo, Felder and Tomassini explained how the notion of formality can be used to construct flat Fedosov connections on formal vector bundles on a Poisson manifold $M$ and thus a star product on $M$ through the original Fedosov method for symplectic manifolds. In this paper, we suppose that $M$ is a fibre bundle manifold equipped with a Poisson tensor tangential to the fibers. We show that in this case the construction of Cattaneo-Felder- Tomassini gives tangential (to the fibers) star products.

Isoperimetric inequality via Lipschitz regularity of Cheeger-harmonic functions

2014

Abstract Let ( X , d , μ ) be a complete, locally doubling metric measure space that supports a local weak L 2 -Poincare inequality. We show that optimal gradient estimates for Cheeger-harmonic functions imply local isoperimetric inequalities.