Prefactorized subgroups in pairwise mutually permutable products

The final publication is available at Springer via http://dx.doi.org/10.1007/s10231-012-0257-yWe continue here our study of pairwise mutually and pairwise totally permutable products. We are looking for subgroups of the product in which the given factorization induces a factorization of the subgroup. In the case of soluble groups, it is shown that a prefactorized Carter subgroup and a prefactorized system normalizer exist.Aless stringent property have F-residual, F-projector and F-normalizer for any saturated formation F including the supersoluble groups.The first and fourth authors have been supported by the grant MTM2010-19938-C03-01 from MICINN (Spain).Ballester-Bolinches, A.; Beidleman, J.; Heineken, H.; Pedraza Aguilera, MC. (2013). Prefactorized subgroups in pairwise mutually permutable products. Annali di Matematica Pura ed Applicata. 192(6):1043-1057. https://doi.org/10.1007/s10231-012-0257-yS104310571926Amberg B., Franciosi S., de Giovanni F.: Products of Groups. Clarendon Press, Oxford (1992)Ballester-Bolinches, A., Pedraza-Aguilera, M.C., Pérez-Ramos, M.D.: Totally and Mutually Permutable Products of Finite Groups, Groups St. Andrews 1997 in Bath I. London Math. Soc. Lecture Note Ser. 260, 65–68. Cambridge University Press, Cambridge (1999)Ballester-Bolinches A., Pedraza-Aguilera M.C., Pérez-Ramos M.D.: On finite products of totally permutable groups. Bull. Aust. Math. Soc. 53, 441–445 (1996)Ballester-Bolinches A., Pedraza-Aguilera M.C., Pérez-Ramos M.D.: Finite groups which are products of pairwise totally permutable subgroups. Proc. Edinb. Math. Soc. 41, 567–572 (1998)Ballester-Bolinches A., Beidleman J.C., Heineken H., Pedraza-Aguilera M.C.: On pairwise mutually permutable products. Forum Math. 21, 1081–1090 (2009)Ballester-Bolinches A., Beidleman J.C., Heineken H., Pedraza-Aguilera M.C.: Local classes and pairwise mutually permutable products of finite groups. Documenta Math. 15, 255–265 (2010)Beidleman J.C., Heineken H.: Mutually permutable subgroups and group classes. Arch. Math. 85, 18–30 (2005)Beidleman J.C., Heineken H.: Group classes and mutually permutable products. J. Algebra 297, 409–416 (2006)Carocca A.: p-supersolvability of factorized groups. Hokkaido Math. J. 21, 395–403 (1992)Carocca, A., Maier, R.: Theorems of Kegel-Wielandt Type Groups St. Andrews 1997 in Bath I. London Math. Soc. Lecture Note Ser. 260, 195–201. Cambridge University Press, Cambridge, (1999)Doerk K., Hawkes T.: Finite Soluble Groups. Walter De Gruyter, Berlin (1992)Maier R., Schmid P.: The embedding of quasinormal subgroups in finite groups. Math. Z. 131, 269–272 (1973

Maximal subgroups and PST-groups

A subgroup H of a group G is said to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable groups, and maximal subgroups, Arch. Math. (Basel), 2011, 96(1), 19-25] presented some new characterisations of soluble T-groups. The main goal of this paper is to establish PT- and PST-versiosn of Kaplan's results, which enables a better understanding of the relationships between these classes

On a class of generalised Schmidt groups

In this paper families of non-nilpotent subgroups covering the non-nilpotent part of a finite group are considered. An $A_5$-free group possessing one of these families is soluble, and soluble groups with this property have Fitting length at most three. A bound on the number of primes dividing the order of the group is also obtained

A Four-Way Comparison of Cardiac Function with Normobaric Normoxia, Normobaric Hypoxia, Hypobaric Hypoxia and Genuine High Altitude.

There has been considerable debate as to whether different modalities of simulated hypoxia induce similar cardiac responses.This was a prospective observational study of 14 healthy subjects aged 22-35 years. Echocardiography was performed at rest and at 15 and 120 minutes following two hours exercise under normobaric normoxia (NN) and under similar PiO2 following genuine high altitude (GHA) at 3,375m, normobaric hypoxia (NH) and hypobaric hypoxia (HH) to simulate the equivalent hypoxic stimulus to GHA.All 14 subjects completed the experiment at GHA, 11 at NN, 12 under NH, and 6 under HH. The four groups were similar in age, sex and baseline demographics. At baseline rest right ventricular (RV) systolic pressure (RVSP, p = 0.0002), pulmonary vascular resistance (p = 0.0002) and acute mountain sickness (AMS) scores were higher and the SpO2 lower (p<0.0001) among all three hypoxic groups (GHA, NH and HH) compared with NN. At both 15 minutes and 120 minutes post exercise, AMS scores, Cardiac output, septal S', lateral S', tricuspid S' and A' velocities and RVSP were higher and SpO2 lower with all forms of hypoxia compared with NN. On post-test analysis, among the three hypoxia groups, SpO2 was lower at baseline and 15 minutes post exercise with GHA (89.3±3.4% and 89.3±2.2%) and HH (89.0±3.1 and (89.8±5.0) compared with NH (92.9±1.7 and 93.6±2.5%). The RV Myocardial Performance (Tei) Index and RVSP were significantly higher with HH than NH at 15 and 120 minutes post exercise respectively and tricuspid A' was higher with GHA compared with NH at 15 minutes post exercise.GHA, NH and HH produce similar cardiac adaptations over short duration rest despite lower SpO2 levels with GHA and HH compared with NH. Notable differences emerge following exercise in SpO2, RVSP and RV cardiac function

Alveolar hypoxia, alveolar macrophages, and systemic inflammation

Diseases featuring abnormally low alveolar PO2 are frequently accompanied by systemic effects. The common presence of an underlying inflammatory component suggests that inflammation may contribute to the pathogenesis of the systemic effects of alveolar hypoxia. While the role of alveolar macrophages in the immune and defense functions of the lung has been long known, recent evidence indicates that activation of alveolar macrophages causes inflammatory disturbances in the systemic microcirculation. The purpose of this review is to describe observations in experimental animals showing that alveolar macrophages initiate a systemic inflammatory response to alveolar hypoxia. Evidence obtained in intact animals and in primary cell cultures indicate that alveolar macrophages activated by hypoxia release a mediator(s) into the circulation. This mediator activates perivascular mast cells and initiates a widespread systemic inflammation. The inflammatory cascade includes activation of the local renin-angiotensin system and results in increased leukocyte-endothelial interactions in post-capillary venules, increased microvascular levels of reactive O2 species; and extravasation of albumin. Given the known extrapulmonary responses elicited by activation of alveolar macrophages, this novel phenomenon could contribute to some of the systemic effects of conditions featuring low alveolar PO2

Strengthening altitude knowledge: a delphi study to define minimum knowledge of altitude illness for laypersons traveling to high altitude

Introduction: A lack of knowledge among laypersons about the hazards of high-altitude exposure contributes to morbidity and mortality from acute mountain sickness (AMS), high-altitude cerebral edema (HACE), and high-altitude pulmonary edema (HAPE) among high-altitude travelers. There are guidelines regarding the recognition, prevention, and treatment of acute-altitude illness for experts, but essential knowledge for laypersons traveling to high altitudes has not been defined. We sought expert consensus on the essential knowledge required for people planning to travel to high altitudes. Methods: The Delphi method was used. The panel consisted of two moderators, a core expert group and a plenary expert group. The moderators made a preliminary list of statements defining the desired minimum knowledge for laypersons traveling to high altitudes, based on the relevant literature. These preliminary statements were then reviewed, supplemented, and modified by a core expert group. A list of 33 statements was then presented to a plenary group of experts in successive rounds. Results: It took three rounds to reach a consensus. Of the 10 core experts invited, 7 completed all the rounds. Of the 76 plenary experts, 41 (54%) participated in Round 1, and of these 41 a total of 32 (78%) experts completed all three rounds. The final list contained 28 statements in 5 categories (altitude physiology, sleeping at altitude, AMS, HACE, and HAPE). This list represents an expert consensus on the desired minimum knowledge for laypersons planning high-altitude travel. Conclusion: Using the Delphi method, the STrengthening Altitude Knowledge initiative yielded a set of 28 statements representing essential learning objectives for laypersons who plan to travel to high altitudes. This list could be used to develop educational interventions