Showing papers by "Adolfo Ballester-Bolinches published in 2009"
TL;DR: In this paper, the influence of the partial cover and avoidance property on the subgroups of some relevant families of subgroups in a finite group has been studied, and the influence is investigated.
Abstract: In this paper we study the influence of the partial cover and avoidance property on the subgroups of some relevant families of subgroups in a finite group.
47 citations
19 citations
TL;DR: In this paper, the authors analyse the impact of strong cover and avoidance property of the members of some relevant families of subgroups on the structure of a group, and show that strong cover avoidance is correlated with strong CAP.
Abstract: A subgroup A of a group G has the strong cover-avoidance property in G, or A is a strong CAP-subgroup of G, if A either covers or avoids every chief factor of every subgroup of G containing A. The main aim of the present paper is to analyse the impact of the strong cover and avoidance property of the members of some relevant families of subgroups on the structure of a group.
15 citations
TL;DR: In this paper, the structure of finite groups whose non-subnormal subgroups lie in some subclasses of the class of finite supersoluble groups is studied. But the main focus of this paper is to study the subgroup structure of the subgroups.
8 citations
TL;DR: In this article, it was shown that the product of pairwise mutually permutable subgroups behaves well with respect to some well-known classes of groups and that all factors have only simple chief factors if the product has this property.
Abstract: Abstract Some results about products of pairwise mutually permutable subgroups are presented in this paper. It is shown that this kind of products behaves well with respect to some well-known classes of groups. For instance, we show that all factors have only simple chief factors if the product has this property. This is necessary but not sufficient: we need that the factors belong to the subclass of PST-groups to make sure that the product has only simple chief factors (see Theorems 5 and 6).
7 citations
TL;DR: In this article, it was shown that the finite modular p-groups, p a prime, are the p-group in which every subnormal subgroup of defect two is permutable or, equivalently, in which each normal subgroup is permuto sensitive.
Abstract: The aim of this paper is to prove certain characterization theorems for groups in which permutability is a transitive relation, the so called \({\mathcal{PT}}\)-groups. In particular, it is shown that the finite solvable \({\mathcal{PT}}\)-groups, the finite solvable groups in which every subnormal subgroup of defect two is permutable, the finite solvable groups in which every normal subgroup is permutable sensitive, and the finite solvable groups in which conjugate-permutability and permutability coincide are all one and the same class. This follows from our main result which says that the finite modular p-groups, p a prime, are those p-groups in which every subnormal subgroup of defect two is permutable or, equivalently, in which every normal subgroup is permutable sensitive. However, there exist finite insolvable groups which are not \({\mathcal{PT}}\)-groups but all subnormal subgroups of defect two are permutable.
5 citations
01 Jan 2009
TL;DR: In this paper, the research grants MTM2004-08219-C02-02 and MTM2007-68010-C03-02 from MEC (Spain) and FEDER (European Union), and GV/2007/243 from Generalitat (Valencia).
Abstract: This paper has been suported by the research grants MTM2004-08219-C02-02 and MTM2007-68010-C03-02 from MEC (Spain) and FEDER (European Union), and GV/2007/243 from Generalitat (Valencia).
3 citations
01 Jul 2009
TL;DR: In this paper, the authors describe an apparatus for processing a substrate 20, which comprises an integrated pumping system 155 having a high operating efficiency, small size, and low vibrational and noise levels.
Abstract: An apparatus 115 for processing a substrate 20, comprises an integrated pumping system 155 having a high operating efficiency, small size, and low vibrational and noise levels. The apparatus 115 comprises a chamber, such as a load-lock chamber 110, transfer chamber 115, or process chamber 120. An integrated pump 165 is abutting or adjacent to one of the chambers 110, 115, 120 for evacuating gas from the chambers. In operation, the pump is located within the actual envelope or footprint of the apparatus and has an inlet 170 connected to a chamber 110, 115, 120, and an outlet 175 that exhausts the gas to atmospheric pressure. Preferably, the integrated pump 165 comprises a pre-vacuum pump or a low vacuum pump and is housed in a noise reducing enclosure having means for moving the pump between locations and means for stacking pumps vertically in use.
3 citations
01 Jan 2009
TL;DR: In this article, the authors present some recent results about pairwise mutually permutable products and classes of groups related to the saturated formation of all supersoluble groups, and show that these products and groups can be classified into several classes.
Abstract: In this paper we present some recent results about pairwise mutually permutable products and classes of groups related to the saturated formation of all supersoluble groups.
2 citations
TL;DR: De Gruyter et al. as mentioned in this paper published a Journal of Group Theory, 12(6):961-963 (2009), with a focus on group theory.
Abstract: This paper has been published in Journal of Group Theory, 12(6):961-963 (2009).
Copyright 2009 by Walter de Gruyter.
The final publication is available at www.degruyter.com.
http://dx.doi.org/10.1515/JGT.2009.026
http://www.degruyter.com/view/j/jgth.2009.12.issue-6/jgt.2009.026/jgt.2009.026.xml
2 citations
TL;DR: In this article, the factorizations of one-generated local and Baer-local formations are studied. But the results are restricted to a class of simple groups, and they are not generalizable to other groups.
Abstract: Under study are the factorizations of one-generated \( \mathfrak{X} \)-local formations, where \( \mathfrak{X} \) is a class of simple groups. Some known results on one-generated local and Baer-local formations appear as particular cases.
01 Jan 2009
TL;DR: Theorem 3.1 as discussed by the authors states that the groups in which all subnormal subgroups areS-permutable (PST-groups) are exactly those groups that are T -groups.
Abstract: Theorem A states that the finite groups in which all subnormal subgroups areS-permutable (PST-groups) are exactly those groups in which subnormal sub-groups of defect 2 are S-permutable (T -groups). The proof uses a characterizationof finite PST-groups in [4], namely the PST-version of Theorem 3.1 (see Post-script). However, the hypothesis of this result was incorrectly stated: the inequality1cr < k should read 0cr < k. Unfortunately, with the weaker hypothesis theresult becomes false, as the following example shows:Example 1. Let A be a group such that ZðAÞ¼FðAÞGC