Antonio Vera López

CLASSIFICATION OF FINITE GROUPS ACCORDING TO THE NUMBER OF CONJUGACY CLASSES II

We consider the problem of the classification of finite groups according to the number of conjugacy classes through the classification of all the finite groups with many minimal normal subgroups.

Efficacy of selective percutaneous embolization for the treatment of intractable posterior epistaxis and juvenile nasopharyngeal angiofibroma (JNA)

Conclusion. Percutaneous embolization reduces the reappearance of epistaxis and the mean length of hospital stay for patients with intractable epistaxis or juvenile nasopharyngeal angiofibroma (JNA). Objectives. To assess whether percutaneous embolization is effective for the treatment of intractable epistaxis and JNA. Patients and methods. Twenty-eight patients with intractable posterior epistaxis treated by embolization (25 males; m = 59.78 years; SD = 14.3) and 28 unembolized patients (24 males; m = 59.21 years; SD = 15.13) were studied retrospectively. Eight patients with JNA (all males; mean = 16.5 years; SD = 2.35; four embolized before surgery and four unembolized) were also analyzed. Results. Embolization was bilateral in 71.4% of subjects, blood transfusion was required in 28.57%, incidence of complications was 53.57%, and seven of the embolized patients with intractable epistaxis suffered from recurrence of the epistaxis. There were no statistically significant differences between the embolized and unembolized groups. The mean hospital stay was longer in unembolized patients (4.46 days; SD = 2.42) than for the embolized patients (3.78 days; SD = 3.9), p=0.394. The most serious complications occurred in patients embolized with idiopathic epistaxis and the mean post-embolization hospital stay was longer in this subgroup (4.14 days; SD = 4.39) than in patients with Rendu-Osler-Weber syndrome (2.40 days; SD = 1.140), p=0.395. Unembolized patients with JNA presented greater hemorrhage (m = 2025 ml; SD = 325) and a longer mean hospital stay (m = 18 days; SD = 3) than the group of embolized patients (m = 360 ml; SD = 185 and m = 9 days; SD = 1, respectively).

On the number of conjugacy classes in a finite group

In the following, G will denote a finite group and we will use the standard notation of the Theory of Groups. We say that G is a D,-group, if G contains a unique conjugacy class of maximal rc-subgroups. In addition, a D,-group G is said to be a LX-group, if all epimorphic images of subgroups of G are D,-groups. For example, if G is n-separable, then G is a LX-group. In particular, all rr-solvable groups are L,-groups. In this work, we get new results relative to the conjugacy classes of a finite group G. Let N be a normal subgroup of G, rt a set of prime numbers, r(G) (resp. r”(G)) the number of conjugacy classes of elements (resp. n-elements) of G, rc(G) the set of all different primes dividing IGIl G, the set of all n-elements of G; and G = G/N. In this paper, we analyze the number r”(G) of conjugacy classes of n-elements of G, through the local analysis of the number r;;(gN) of conjugacy classes of n-elements of G which intersect the coset gN. Our aims are threefold: to obtain upper and lower bounds of the number r”(G) of conjugacy classes of rc-elements of G, in terms of the numbers r”(G/N), r”(N), and [G’l, where G’ denotes the derived subgroup of G; to get the residue class of r”(G), modulo the “best” number, given in terms of the primes dividing (GI ; and finally, to analyze the conjugacy-vector d, = (IC,(g,)l, . . . . IC,( g,)l) of G, assuming that G is the disjoint union of the classes Cl,(g,), i= 1, . . . . r=r(G), and lCG(g1)3 ... 3 IC,(g,)l. The results obtained are useful both for the calculation of the conjugacy-vector of a finite group and for the classification of finite groups according to the number of conjugacy classes (see Examples 11-13 in Section 4). Moreover, they enable us to obtain the following inequalities:

Conjugacy classes in finite solvable groups

In this note, we obtain the number of conjugacy classes in a finite solvable group as a function of any tuple of the composition factors ofG. Using this relation, we give a new elementary proof of one of Manns results for solvable groups, without using character theory, and we improve this result for some classes of groups.

Arithmetical conditions on the conjugacy vector of a finite group

We get new properties of the numbersr G(xN) = |{Cl G (g)|Cl G (g)∩xN ≠ O} (whereG is a finite group andN is a normal subgroup ofG) that are useful in the analysis of the classification of the finite groups according to the number of conjugacy classes.We get new properties of the numbersrG(xN) = |{ClG(g)|ClG(g)∩xN ≠ Ø} (whereG is a finite group andN is a normal subgroup ofG) that are useful in the analysis of the classification of the finite groups according to the number of conjugacy classes.

Generating Persistence Structures for the Integration of Data and Control Aspects in Business Process Monitoring.

Today’s organizations have to monitor increasingly complex business processes that handle large amounts of data. In this context, it is essential to design working frameworks that seamlessly integrate both control flow and data perspectives. Such an integration can be eased by automatically generating the infrastructures for storing data and control aspects. Towards this goal, we propose an automatic process for synthesizing persistence structures for control flow and data storage. In particular, based on an approach centered on the concept of Occurrence, in this paper we present a proposal by means of which, after applying several translation patterns to a business process model, we automatically generate the persistence structures that integrate both data and control aspects of such model. The feasibility of this proposal is demonstrated by developing a prototype and evaluating its application to different examples taken from the literature as a benchmark.

Developing provenance-aware query systems: an occurrence-centric approach

In recent years, research on provenance has increased exponentially, and such studies in the field of business process monitoring have been especially remarkable. Business process monitoring deals with recording information about the actual execution of processes to then extract valuable knowledge that can be utilized for business process quality improvement. In prior research, we developed an occurrence-centric approach built on our notion of occurrence that provides a holistic perspective of system dynamics. Based on this concept, more complex structures are defined herein, namely Occurrence Base (OcBase) and Occurrence Management System (OcSystem), which serve as scaffolding to develop business process monitoring systems. This paper focuses primarily on the critical provenance task of extracting valuable knowledge from such systems by proposing an Occurrence Query Framework that includes the definition of an Occurrence Base Metamodel and an Occurrence Query Language based on this metamodel. Our framework provides a way of working for the construction of business process monitoring systems that are provenance aware. As a proof of concept, a tool implementing the various components of the framework is presented. This tool has been tested against a real system in the context of biobanks.

About the finite groups whose minimal normal subgroups are union of two conjugacy classes exactly

SummaryIn this paper we classify all the finite groups G satisfying β(G)=r(G) — α(G) - 1 where r(G) is the number of conjugacy classes of G, β(G) the number of minimal normal subgroups of G, S(G) the socle of G and α(G) the number of conjugacy classes of G out of S(G), and such that ¦G/S(G)¦ is divisible for at most three prime numbers.