Search results for "combinatoric"

On 𝓕-subnormal subgroups and Frattini-like subgroups of a finite group

1994

Throughout the paper we consider only finite groups.J. C. Beidleman and H. Smith [3] have proposed the following question: “If G is a group and Ha subnormal subgroup of G containing Φ(G), the Frattini subgroup of G, such that H/Φ(G)is supersoluble, is H necessarily supersoluble? “In this paper, we give not only an affirmative answer to this question but also we see that the above result still holds if supersoluble is replaced by any saturated formation containing the class of all nilpotent groups.

On-line construction of two-dimensional suffix trees

1997

We present a new technique, which we refer to as implicit updates, based on which we obtain: (a) an algorithm for the on-line construction of the Lsuffix tree of an n x n matrix A — this data structure, described in [13], is the two-dimensional analog of the suffix tree of a string; (b) simple algorithms implementing primitive operations for LZ1-type on-dine lossless image compression methods. Those methods, recently introduced by Storer [35], are generalizations of LZl-type compression methods for strings (see also [24, 31]). For the problem in (a), we get nearly an order of magnitude improvement over algorithms that can be derived from known techniques [13]. For the problem in (b), we do …

On the divisor class group of double solids

1999

For a double solid V→ℙ3> branched over a surface B⊂ℙ3(ℂ) with only ordinary nodes as singularities, we give a set of generators of the divisor class group \(\) in terms of contact surfaces of B with only superisolated singularities in the nodes of B. As an application we give a condition when H* (˜V , ℤ) has no 2-torsion. All possible cases are listed if B is a quartic. Furthermore we give a new lower bound for the dimension of the code of B.

Groups whose real irreducible characters have degrees coprime to p

2012

Abstract In this paper we study groups for which every real irreducible character has degree not divisible by some given odd prime p .

A series of finite groups and related symmetric designs

2007

For any odd prime power q = pe we study a certain solvable group G of order q2 · ((q-1)/2)2 · 2 and construct from its internal structure a symmetric design D with parameters (2q2+1, q2, (q2-1)/2) on which G acts as an automorphism group. As a consequence we find that the full automorphism group of D contains a subgroup of order |G| · e2.

Explicit expressions for totally symmetric spherical functions and symmetry-dependent properties of multipoles

2014

Closed expressions for matrix elements 〈 lm' | A (G)| lm 〉, where | lm 〉 are spherical functions and A (G) is the average of all symmetry operators of point group G, are derived for all point groups (PGs) and then used to obtain linear combinations of spherical functions that are totally symmetric under all symmetry operations of G. In the derivation, we exploit the product structure of the groups. The obtained expressions are used to explore properties of multipoles of symmetric charge distributions. We produce complete lists of selection rules for multipoles Q l and their moments Q lm , as well as of numbers of independent moments in a multipole, for any l and m and for all PGs. Periodic…

Norms of harmonic projection operators on compact Lie groups

1988

In order to simplify the notation, we will assume throughout that G is connected, simply connected and semisimple. Sharp estimates for vp(z 0 when G = SU(2) have been obtained by Sogge [6], who proved that Vp(Zt) ~ d~ tl/v), where y(t) is the function which is affine on [1/2, 3/4] and on [3/4, 1] and is such that 7(1/2)=0, 7(3/4)=1/4, 7(1)=1. Two results in the literature give crucial estimates from below for vp(n) in the general case. The first estimate concernes the LP'-norm of the character X, : if ,~, is the highest weight of n and 0 is half the sum of the positive roots, then II x=llp,--> + 011-dimG/p" (1.2)

Co-jumps and Markov Counting Systems in Random Environments

2020

Motivated by the analysis of multi-strain infectious disease data, we provide closed-form transition rates for continuous-time Markov chains that arise from subjecting Markov counting systems to correlated environmental noises. Noise correlation induces co-jumps or counts that occur simultaneously in several counting processes. Such co-jumps are necessary and sufficient for infinitesimal correlation between counting processes of the system. We analyzed such infinitesimal correlation for a specific infectious disease model by randomizing time of Kolmogorov’s Backward system of differential equations based on appropriate stochastic integrals.

Equidistribution of Common Perpendicular Arcs

2019

In this chapter, we prove the equidistribution of the initial and terminal vectors of common perpendiculars of convex subsets, at the universal covering space level, for Riemannian manifolds and for metric and simplicial trees.

On embedding Boolean as a subtype of integer

1990