On sigma-subnormality criteria in finite sigma-soluble groups

[EN] Let sigma = {sigma(i) : i is an element of I} be a partition of the set P of all prime numbers. A subgroup X of a finite group G is called sigma-subnormal in G if there is a chain of subgroups X = X-0 subset of X-1 subset of center dot center dot center dot subset of X-n = G where for every j = 1,..., n the subgroup X j-1 is normal in X j or X j /CoreX j ( X j-1) is a si -group for some i. I. In the special case that s is the partition of P into sets containing exactly one prime each, the sigma-subnormality reduces to the familiar case of subnormality. In this paper some sigma-subnormality criteria for subgroups of s-soluble groups, or groups in which every chief factor is a sigma(i)-group, for some sigma(i) sigma s, are showed.The first and third authors are supported by the grant PGC2018-095140-B-I00 from the Ministerio de Ciencia, Innovacion y Universidades and the Agencia Estatal de Investigacion, Spain, and FEDER, European Union and Prometeo/2017/057 of Generalitat (Valencian Community, Spain). The second author was supported by the State Program of Science Researchers of the Republic of Belarus (Grant 19-54 "Convergence-2020").Ballester-Bolinches, A.; Kamornikov, SF.; Pedraza Aguilera, MC.; Pérez-Calabuig, V. (2020). On sigma-subnormality criteria in finite sigma-soluble groups. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(2):1-9. https://doi.org/10.1007/s13398-020-00824-4S191142Amberg, B., Franciosi, S., De Giovanni, F.: Products of Groups. Oxford Mathematical Monographs. Clarendon Press, Oxford (1992)Ballester-Bolinches, A., Ezquerro, L.M.: Classes of Finite Groups, Vol. 584 of Mathematics and its Applications. Springer, New York (2006)Ballester-Bolinches, A., Kamornikov, S.F., Pedraza-Aguilera, M.C., Yi, X.: On -subnormal subgroups of factorised finite groups (Preprint)Casolo, C.: Subnormality in factorizable finite soluble groups. Arch. Math. 57, 12–13 (1991)Doerk, K., Hawkes, T.: Finite Soluble Groups. Walter De Gruyter, Berlin (1992)Fumagalli, Francesco: On subnormality criteria for subgroups in finite groups. J. Lond. Math. Soc. 76(2), 237–252 (2007)Kamornikov, S.F., Shemetkova, O.L.: On $${{\cal{F}}}$$-subnormal subgroups of a finite factorised group. Probl. Phys. Math. Tech. 1, 61–63 (2018)Khukhro, E.I., Mazurov, V.D.: Unsolved Problems in Group Theory. The Kourovka notebook. Institut Matematiki SO RAN, Novosibirsk, No. 19 (2018)Lennox, J.C., Stonehewer, S.E.: Subnormal Subgroups of Groups. Clarendon Press, Oxford (1987)Maier, R.: Um problema da teoria dos subgrupos subnormais. Bol. Soc. Bras. Mat. 8(2), 127–130 (1977)Maier, R., Sidki, R.: A note on subnormality in factorizable finite groups. Arch. Math. 42, 97–101 (1984)Skiba, A.N.: A generalization of a Hall theorem. J. Algebra Appl. 15(4), 13 (2016)Skiba, A.N.: On $$\sigma$$-subnormal and $$\sigma$$-permutable subgroups of finite groups. J. Algebra 436, 1–16 (2015)Skiba, A.N.: On -properties of finite groups I. Probl. Phys. Math. Tech. 4, 89–96 (2014)Skiba, A.N.: On -properties of finite groups II. Probl. Phys. Math. Tech. 3(24), 70–83 (2015)Skiba, A.N.: On some arithmetic properties of finite groups. Note Mat. 36, 65–89 (2016)Wielandt, H.: Subnormalität in faktorisierten endlichen Grupppen. J. Algebra 69, 305–311 (1981

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

The Extent and Coverage of Current Knowledge of Connected Health: Systematic Mapping Study

Background: This paper examines the development of the Connected Health research landscape with a view on providing a historical perspective on existing Connected Health research. Connected Health has become a rapidly growing research field as our healthcare system is facing pressured to become more proactive and patient centred. Objective: We aimed to identify the extent and coverage of the current body of knowledge in Connected Health. With this, we want to identify which topics have drawn the attention of Connected health researchers, and if there are gaps or interdisciplinary opportunities for further research. Methods: We used a systematic mapping study that combines scientific contributions from research on medicine, business, computer science and engineering. We analyse the papers with seven classification criteria, publication source, publication year, research types, empirical types, contribution types research topic and the condition studied in the paper. Results: Altogether, our search resulted in 208 papers which were analysed by a multidisciplinary group of researchers. Our results indicate a slow start for Connected Health research but a more recent steady upswing since 2013. The majority of papers proposed healthcare solutions (37%) or evaluated Connected Health approaches (23%). Case studies (28%) and experiments (26%) were the most popular forms of scientific validation employed. Diabetes, cancer, multiple sclerosis, and heart conditions are among the most prevalent conditions studied. Conclusions: We conclude that Connected Health research seems to be an established field of research, which has been growing strongly during the last five years. There seems to be more focus on technology driven research with a strong contribution from medicine, but business aspects of Connected health are not as much studied

Observation of an Excited Bc+ State

Using pp collision data corresponding to an integrated luminosity of 8.5 fb-1 recorded by the LHCb experiment at center-of-mass energies of s=7, 8, and 13 TeV, the observation of an excited Bc+ state in the Bc+π+π- invariant-mass spectrum is reported. The observed peak has a mass of 6841.2±0.6(stat)±0.1(syst)±0.8(Bc+) MeV/c2, where the last uncertainty is due to the limited knowledge of the Bc+ mass. It is consistent with expectations of the Bc∗(2S31)+ state reconstructed without the low-energy photon from the Bc∗(1S31)+→Bc+γ decay following Bc∗(2S31)+→Bc∗(1S31)+π+π-. A second state is seen with a global (local) statistical significance of 2.2σ (3.2σ) and a mass of 6872.1±1.3(stat)±0.1(syst)±0.8(Bc+) MeV/c2, and is consistent with the Bc(2S10)+ state. These mass measurements are the most precise to date

Measurement of b hadron fractions in 13 TeV pp collisions

The production fractions of ¯ B 0 s and Λ 0 b hadrons, normalized to the sum of B − and ¯ B 0 fractions, are measured in 13 TeV p p collisions using data collected by the LHCb experiment, corresponding to an integrated luminosity of 1.67     fb − 1 . These ratios, averaged over the b hadron transverse momenta from 4 to 25 GeV and pseudorapidity from 2 to 5, are 0.122 ± 0.006 for ¯ B 0 s , and 0.259 ± 0.018 for Λ 0 b , where the uncertainties arise from both statistical and systematic sources. The Λ 0 b ratio depends strongly on transverse momentum, while the ¯ B 0 s ratio shows a mild dependence. Neither ratio shows variations with pseudorapidity. The measurements are made using semileptonic decays to minimize theoretical uncertainties. In addition, the ratio of D + to D 0 mesons produced in the sum of ¯ B 0 and B − semileptonic decays is determined as 0.359 ± 0.006 ± 0.009 , where the uncertainties are statistical and systematic

Observation of B(s)0→J/ψpp¯ decays and precision measurements of the B(s)0 masses

The first observation of the decays B 0 ( s ) → J / ψ p ¯ p is reported, using proton-proton collision data corresponding to an integrated luminosity of 5.2     fb − 1 , collected with the LHCb detector. These decays are suppressed due to limited available phase space, as well as due to Okubo-Zweig-Iizuka or Cabibbo suppression. The measured branching fractions are B ( B 0 → J / ψ p ¯ p ) = [ 4.51 ± 0.40 ( stat ) ± 0.44 ( syst ) ] × 10 − 7 , B ( B 0 s → J / ψ p ¯ p ) = [ 3.58 ± 0.19 ( stat ) ± 0.39 ( syst ) ] × 10 − 6 . For the B 0 s meson, the result is much higher than the expected value of O ( 10 − 9 ) . The small available phase space in these decays also allows for the most precise single measurement of both the B 0 mass as 5279.74 ± 0.30 ( stat ) ± 0.10 ( syst )     MeV and the B 0 s mass as 5366.85 ± 0.19 ( stat ) ± 0.13 ( syst )     MeV

Measurement of the Charm-Mixing Parameter yCP

A measurement of the charm-mixing parameter y_{CP} using D^{0}→K^{+}K^{-}, D^{0}→π^{+}π^{-}, and D^{0}→K^{-}π^{+} decays is reported. The D^{0} mesons are required to originate from semimuonic decays of B^{-} and B[over ¯]^{0} mesons. These decays are partially reconstructed in a data set of proton-proton collisions at center-of-mass energies of 7 and 8 TeV collected with the LHCb experiment and corresponding to an integrated luminosity of 3  fb^{-1}. The y_{CP} parameter is measured to be (0.57±0.13(stat)±0.09(syst))%, in agreement with, and as precise as, the current world-average value

Erratum to: Measurement of ϒ production in pp collisions at s√ = 13 TeV

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