On a question of Beidleman and Robinson

In (1, Theorem A), Beidleman and Robinson proved that if a group satisfies the permutizer condition, it is soluble, its chief factors have order a prime number or 4 and G induces the full group of automorphisms in the chief factors of order 4. In this paper, we show that the converse of this theorem is false by showing some counterexamples. We also find some sufficient conditions for a group satisfying the converse of that theorem to satisfy the permutizer condition

Large characteristically simple sections of finite groups

In this paper we prove that if G is a group for which there are k non-Frattini chief factors isomorphic to a characteristically simple group A, then G has a normal section C/R that is the direct product of k minimal normal subgroups of G/R isomorphic to A. This is a significant extension of the notion of crown for isomorphic chief factors

Bounds on the number of maximal subgroups of finite groups: applications

The determination of bounds for the number of maximal subgroups of a given index in a finite group is relevant to estimate the number of random elements needed to generate a group with a given probability. In this paper, we obtain new bounds for the number of maximal subgroups of a given index in a finite group and we pin-point the universal constants that appear in some results in the literature related to the number of maximal subgroups of a finite group with a given index. This allows us to compare properly our bounds with some of the known bounds

Enumeration of left braces with additive group C2×C2×C4×C4C_2\times C_2\times C_4\times C_4

We show that the number of isomorphism classes of left braces of order~$64$ with additive group isomorphic to $C_2\times C_2\times C_4\times C_4$ is $10\,326\,821$. This completes the classification of left braces of order~$64$, that turn out to fall into $15\,095\,601$ isomorphism classes.Comment: Ric. Mat., in press. 9 pages. arXiv admin note: substantial text overlap with arXiv:2210.1282

Some solubility criteria in factorised groups

This paper has been published in Bulletin of the Australian Mathematical Society, 86(1):22-28 (2012). Copyright 2012 by Australian Mathematical Publishing Association Inc and Cambridge University Press Journals. The final publication is available at http://journals.cambridge.org/abstract_S0004972711003418In this paper, solubility of groups factorised as a product of two subgroups which are connected by certain permutability properties is studied.The research of the second and the third authors has been supported by the grant MTM2010-19938-C03-01 from the Ministerio de Ciencia e Innovacion (Spanish government).http://dx.doi.org/10.1017/S0004972711003418Asaad, M.; Ballester Bolinches, A.; Esteban Romero, R. (2012). Some solubility criteria in factorised groups. Bulletin of the Australian Mathematical Society. (86). doi:10.1017/S0004972711003418S8

Production of gamma rays and neutrinos in the dark jets of the microquasar SS433

We study the spectral energy distribution of gamma rays and neutrinos in the precessing microquasar SS433 as a result of pp interactions within its dark jets. Gamma-ray absorption due to interactions with matter of the extended disc and of the star is found to be important, as well as absorption caused by the ultraviolet and mid-infrared radiation from the equatorial envelopment. We analyse the range of precessional phases for which this attenuation is at a minimum and the chances for detection of a gamma-ray signal are enhanced. The power of relativistic protons in the jets, a free parameter of the model, is constrained by HEGRA data. This imposes limits on the gamma-ray fluxes to be detected with instruments such as GLAST, VERITAS and MAGIC II. A future detection of high-energy neutrinos with cubic kilometre telescopes such as IceCube would also yield important information about acceleration mechanisms that may take place in the dark jets. Overall, the determination of the ratio of gamma-ray to neutrino flux will result in a key observational tool to clarify the physics of heavy jets.Facultad de Ciencias Astronómicas y GeofísicasInstituto Argentino de Radioastronomí

Molecular clouds as reservoir of cosmic rays

Giant molecular clouds (GMCs) are emerging as a new population of -ray sources; with detections by instruments such as HESS and Fermi. These dense clouds are targets for cosmic rays (CRs) -- locally accelerated or not --. GMCs host very young star clusters where massive star formation takes place. Some of the early-type stars are usually ejected from the clusters; becoming runaway stars; that move through the cloud. These stars develop bowshocks where particles can be accelerated up to relativistic energies. As a result; the bowshocks present radio to -ray emission of leptonic origin; and inject relativistic protons in the cloud. These protons diffuse in the GMC interacting with the matter via inelastic collisions. This gives rise to extended -ray sources. We present a model for the non-thermal radiation produced by locally accelerated CRs in GMCs.Instituto Argentino de RadioastronomíaFacultad de Ciencias Astronómicas y GeofísicasConsejo Nacional de Investigaciones Científicas y Técnica

Molecular clouds as reservoir of cosmic rays

Giant molecular clouds (GMCs) are emerging as a new population of -ray sources; with detections by instruments such as HESS and Fermi. These dense clouds are targets for cosmic rays (CRs) -- locally accelerated or not --. GMCs host very young star clusters where massive star formation takes place. Some of the early-type stars are usually ejected from the clusters; becoming runaway stars; that move through the cloud. These stars develop bowshocks where particles can be accelerated up to relativistic energies. As a result; the bowshocks present radio to -ray emission of leptonic origin; and inject relativistic protons in the cloud. These protons diffuse in the GMC interacting with the matter via inelastic collisions. This gives rise to extended -ray sources. We present a model for the non-thermal radiation produced by locally accelerated CRs in GMCs.Instituto Argentino de RadioastronomíaFacultad de Ciencias Astronómicas y GeofísicasConsejo Nacional de Investigaciones Científicas y Técnica

Left braces and the quantum Yang-Baxter equation

[EN] Braces were introduced by Rump in 2007 as a useful tool in the study of the set-theoretic solutions of the Yang¿Baxter equation. In fact, several aspects of the theory of finite left braces and their applications in the context of the Yang¿Baxter equation have been extensively investigated recently. The main aim of this paper is to introduce and study two finite brace theoretical properties associated with nilpotency, and to analyse their impact on the finite solutions of the Yang¿Baxter equation.This work was supported by the research grant MTM2014-54707-C3-1-P from the Ministerio de Economia y Competitividad, Spanish Government, and FEDER, European Union, and PROMETEO/2017/057 from Generalitat (Valencian Community, Spain). The first author was supported by grant number 201606890006 of the China Scholarship Council.Meng, H.; Ballester Bolinches, A.; Esteban Romero, R. (2019). Left braces and the quantum Yang-Baxter equation. Proceedings of the Edinburgh Mathematical Society. 62(2):595-608. https://doi.org/10.1017/S0013091518000664S595608622Yang, C. N. (1967). Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction. Physical Review Letters, 19(23), 1312-1315. doi:10.1103/physrevlett.19.1312Smoktunowicz, A. (2018). On Engel groups, nilpotent groups, rings, braces and the Yang-Baxter equation. Transactions of the American Mathematical Society, 370(9), 6535-6564. doi:10.1090/tran/7179Etingof, P., Schedler, T., & Soloviev, A. (1999). Set-theoretical solutions to the quantum Yang-Baxter equation. Duke Mathematical Journal, 100(2), 169-209. doi:10.1215/s0012-7094-99-10007-xCedó, F., Jespers, E., & Okniński, J. (2014). Braces and the Yang–Baxter Equation. Communications in Mathematical Physics, 327(1), 101-116. doi:10.1007/s00220-014-1935-yCedó, F., Gateva-Ivanova, T., & Smoktunowicz, A. (2017). On the Yang–Baxter equation and left nilpotent left braces. Journal of Pure and Applied Algebra, 221(4), 751-756. doi:10.1016/j.jpaa.2016.07.014Bachiller, D., Cedó, F., & Jespers, E. (2016). Solutions of the Yang–Baxter equation associated with a left brace. Journal of Algebra, 463, 80-102. doi:10.1016/j.jalgebra.2016.05.024Rump, W. (2007). Braces, radical rings, and the quantum Yang–Baxter equation. Journal of Algebra, 307(1), 153-170. doi:10.1016/j.jalgebra.2006.03.040Smoktunowicz, A. (2018). A note on set-theoretic solutions of the Yang–Baxter equation. Journal of Algebra, 500, 3-18. doi:10.1016/j.jalgebra.2016.04.015Kurzweil, H., & Stellmacher, B. (2004). The Theory of Finite Groups. Universitext. doi:10.1007/b9743

Molecular clouds as reservoir of cosmic rays

Giant molecular clouds (GMCs) are emerging as a new population of -ray sources; with detections by instruments such as HESS and Fermi. These dense clouds are targets for cosmic rays (CRs) -- locally accelerated or not --. GMCs host very young star clusters where massive star formation takes place. Some of the early-type stars are usually ejected from the clusters; becoming runaway stars; that move through the cloud. These stars develop bowshocks where particles can be accelerated up to relativistic energies. As a result; the bowshocks present radio to -ray emission of leptonic origin; and inject relativistic protons in the cloud. These protons diffuse in the GMC interacting with the matter via inelastic collisions. This gives rise to extended -ray sources. We present a model for the non-thermal radiation produced by locally accelerated CRs in GMCs.Instituto Argentino de RadioastronomíaFacultad de Ciencias Astronómicas y GeofísicasConsejo Nacional de Investigaciones Científicas y Técnica