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

Primitive subgroups and PST-groups

All groups are finite. A subgroup H of a group G is called a primitive subgroup if it is a proper subgroup in the intersection of all subgroups of G containing H as its proper subgroup. He, Qiao and Wang [7] proved that every primitive subgroup of a group G has index a power of a prime if and only if G/Φ(G) is a solvable PST-group. Let X denote the class of groups G all of whose primitive subgroups have prime power index. It is established here that a group G is a solvable PST-group if and only if every subgroup of G is an X-group.Ballester-Bolinches, A.; Beidleman, J.; Esteban Romero, R. (2014). Primitive subgroups and PST-groups. Bulletin of the Australian Mathematical Society. 89(3):373-378. doi:10.1017/S0004972713000592S373378893Holmes, C. V. (1966). A Characterization of Finite Nilpotent Groups. The American Mathematical Monthly, 73(10), 1113. doi:10.2307/2314655Ore, O. (1939). Contributions to the theory of groups of finite order. Duke Mathematical Journal, 5(2), 431-460. doi:10.1215/s0012-7094-39-00537-5Ragland, M. F. (2007). Generalizations of Groups in which Normality Is Transitive. Communications in Algebra, 35(10), 3242-3252. doi:10.1080/00914030701410302Zappa, G. (1940). Remark on a recent paper of O. Ore. Duke Mathematical Journal, 6(2), 511-512. doi:10.1215/s0012-7094-40-00641-xBallester-Bolinches, A., Beidleman, J. C., & Esteban-Romero, R. (2007). On some classes of supersoluble groups. Journal of Algebra, 312(1), 445-454. doi:10.1016/j.jalgebra.2006.07.035Van der Waall, R. W., & Fransman, A. (1996). ON PRODUCTS OF GROUPS FOR WHICH NORMALITY IS A TRANSITIVE RELATION ON THEIR FRATTINI FACTOR GROUPS. Quaestiones Mathematicae, 19(1-2), 59-82. doi:10.1080/16073606.1996.9631826Agrawal, R. K. (1975). Finite groups whose subnormal subgroups permute with all Sylow subgroups. Proceedings of the American Mathematical Society, 47(1), 77-77. doi:10.1090/s0002-9939-1975-0364444-4Robinson, D. J. S. (1996). A Course in the Theory of Groups. Graduate Texts in Mathematics. doi:10.1007/978-1-4419-8594-1Ballester-Bolinches, A., Esteban-Romero, R., & Pedraza-Aguilera, M. C. (2005). On a Class of p-Soluble Groups. Algebra Colloquium, 12(02), 263-267. doi:10.1142/s1005386705000258He, X., Qiao, S., & Wang, Y. (2013). A NOTE ON PRIMITIVE SUBGROUPS OF FINITE SOLVABLE GROUPS. Communications of the Korean Mathematical Society, 28(1), 55-62. doi:10.4134/ckms.2013.28.1.055Johnson, D. L. (1971). A Note on Supersoluble Groups. Canadian Journal of Mathematics, 23(3), 562-564. doi:10.4153/cjm-1971-063-5Humphreys, J. F. (1974). On groups satisfying the converse of Lagrange’s theorem. Mathematical Proceedings of the Cambridge Philosophical Society, 75(1), 25-32. doi:10.1017/s030500410004819

On a class of supersoluble groups

A subgroup H of a finite group G is said to be S-semipermutable in G if H permutes with every Sylow q-subgroup of G for all primes q not dividing |H|. A finite group G is an MS-group if the maximal subgroups of all the Sylow subgroups of G are S-semipermutable in G. The aim of the present paper is to characterise the finite MS-groups

On a class of p-soluble groups

Electronic version of an article published as Algebra Colloquium, 12(2)(2005), 263-267 DOI: 10.1142/S1005386705000258. © copyright World Scientific Publishing Company. http://www.worldscientific.com/doi/abs/10.1142/S1005386705000258[EN] Let p be a prime. The class of all p-soluble groups G such that every p-chief factor of G is cyclic and all p-chief factors of G are G-isomorphic is studied in this paper. Some results on T-, PT-, and PST -groups are also obtained.Supported by Grant BFM2001-1667-C03-03, MCyT (Spain) and FEDER (European Union)http://www.worldscientific.com/doi/abs/10.1142/S1005386705000258Ballester Bolinches, A.; Esteban Romero, R.; Pedraza Aguilera, MC. (2005). On a class of p-soluble groups. Algebra Colloquium. 2(12). doi:10.1142/S100538670500025821

The impact of submaximal exercise during heat and/or hypoxia on the cardiovascular and monocyte HSP72 responses to subsequent (post 24 h) exercise in hypoxia

BACKGROUND: The aims of this study were to describe the cellular stress response to prolonged endurance exercise in acute heat, hypoxia and the combination of heat and hypoxia and to determine whether prior acute exposure to these stressors improved cellular tolerance to a subsequent exercise bout in hypoxia 24 h later. METHODS: Twelve males (age 22 ± 4 years, height 1.77 ± 0.05 m, mass 79 ± 12.9 kg, VO(2) max 3.57 ± 0.7 L · min(-1)) completed four trials (30-min rest, 90-min cycling at 50% normoxic VO(2) max) in normothermic normoxia (NORM; 18°C, F(I)O(2) = 0.21), heat (HEAT; 40°C, 20% RH), hypoxia (HYP; F(I)O(2) = 0.14) or a combination of heat and hypoxia (COM; 40°C, 20% RH, F(I)O(2) = 0.14) separated by at least 7 days. Twenty-four hours after each trial, participants completed a hypoxic stress test (HST; 15-min rest, 60-min cycling at 50% normoxic VO(2) max, F(I)O(2) = 0.14). Monocyte heat shock protein 72 (mHSP72) was assessed immediately before and after each exercise bout. RESULTS: mHSP72 increased post exercise in NORM (107% ± 5.5%, p > 0.05), HYP (126% ± 16%, p < 0.01), HEAT (153% ± 14%, p < 0.01) and COM (161% ± 32%, p < 0.01). mHSP72 had returned to near-resting values 24 h after NORM (97% ± 8.6%) but was elevated after HEAT (130% ± 19%), HYP (118% ± 17%) and COM (131% ± 19%) (p < 0.05). mHSP72 increased from baseline after HST(NORM) (118% ± 12%, p < 0.05), but did not increase further in HST(HEAT), HST(HYP) and HST(COM). CONCLUSIONS: The prior induction of mHSP72 as a result of COM, HEAT and HYP attenuated further mHSP72 induction after HST and was indicative of conferred cellular tolerance

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