Search results for " Group Theory"
showing 10 items of 117 documents
Complete weights andv-peak points of spaces of weighted holomorphic functions
2006
We examine the geometric theory of the weighted spaces of holomorphic functions on bounded open subsets ofC n ,C n ,H v (U) and\(H_{v_o } (U)\), by finding a lower bound for the set of weak*-exposed and weak*-strongly exposed points of the unit ball of\(H_{v_o } (U)'\) and give necessary and sufficient conditions for this set to be naturally homeomorphic toU. We apply these results to examine smoothness and strict convexity of\(H_{v_o } (U)\) and\(H_v (U)\). We also investigate whether\(H_{v_o } (U)\) is a dual space.
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 $\operatorname{l}(S)^2 < |S|$.
Conjugacy problem for braid groups and Garside groups
2003
We present a new algorithm to solve the conjugacy problem in Artin braid groups, which is faster than the one presented by Birman, Ko and Lee. This algorithm can be applied not only to braid groups, but to all Garside groups (which include finite type Artin groups and torus knot groups among others).
Heat Kernel Measure on Central Extension of Current Groups in any Dimension
2006
We define measures on central extension of current groups in any dimension by using infinite dimensional Brownian motion.
Bounds for the relative n-th nilpotency degree in compact groups
2009
The line of investigation of the present paper goes back to a classical work of W. H. Gustafson of the 1973, in which it is described the probability that two randomly chosen group elements commute. In the same work, he gave some bounds for this kind of probability, providing information on the group structure. We have recently obtained some generalizations of his results for finite groups. Here we improve them in the context of the compact groups.
Longest Motifs with a Functionally Equivalent Central Block
2004
International audience; This paper presents a generalization of the notion of longest repeats with a block of k don't care symbols introduced by [Crochemore et al., LATIN 2004] (for k fixed) to longest motifs composed of three parts: a first and last that parameterize match (that is, match via some symbol renaming, initially unknown), and a functionally equivalent central block. Such three-part motifs are called longest block motifs. Different types of functional equivalence, and thus of matching criteria for the central block are considered, which include as a subcase the one treated in [Crochemore et al., LATIN 2004] and extend to the case of regular expressions with no Kleene closure or …
On the number of constituents of products of characters
2022
It has been conjectured that if the number of distinct irreducible constituents of the product of two faithful irreducible characters of a finite p-group, for p ≥ 5, is bigger than (p + 1)/2, then it is at least p. We give a counterexample to this conjecture.
Finite 2-groups with odd number of conjugacy classes
2016
In this paper we consider finite 2-groups with odd number of real conjugacy classes. On one hand we show that if $k$ is an odd natural number less than 24, then there are only finitely many finite 2-groups with exactly $k$ real conjugacy classes. On the other hand we construct infinitely many finite 2-groups with exactly 25 real conjugacy classes. Both resuls are proven using pro-$p$ techniques and, in particular, we use the Kneser classification of semi-simple $p$-adic algebraic groups.
A Classification of all Symmetric Block Designs of Order Nine with an Automorphism of Order Six
2006
We complete the classification of all symmetric designs of order nine admitting an automorphism of order six. As a matter of fact, the classification for the parameters (35,17,8), (56,11,2), and (91,10,1) had already been done, and in this paper we present the results for the parameters (36,15,6), (40,13,4), and (45,12,3). We also provide information about the order and the structure of the full automorphism groups of the constructed designs. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 301–312, 2006
Sensitivity Versus Certificate Complexity of Boolean Functions
2016
Sensitivity, block sensitivity and certificate complexity are basic complexity measures of Boolean functions. The famous sensitivity conjecture claims that sensitivity is polynomially related to block sensitivity. However, it has been notoriously hard to obtain even exponential bounds. Since block sensitivity is known to be polynomially related to certificate complexity, an equivalent of proving this conjecture would be showing that the certificate complexity is polynomially related to sensitivity. Previously, it has been shown that $$bsf \le Cf \le 2^{sf-1} sf - sf-1$$. In this work, we give a better upper bound of $$bsf \le Cf \le \max \left 2^{sf-1}\left sf-\frac{1}{3}\right , sf\right $…