2,064 research outputs found

    Finite p-groups with a Frobenius group of automorphisms whose kernel is a cyclic p-group

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    Suppose that a finite p-group G admits a Frobenius group of automorphisms FH with kernel F that is a cyclic p-group and with complement H. It is proved that if the fixed-point subgroup CG(H) of the complement is nilpotent of class c, then G has a characteristic subgroup of index bounded in terms of c, jCG(F)j, and jFj whose nilpotency class is bounded in terms of c and jHj only. Examples show that the condition of F being cyclic is essential. The proof is based on a Lie ring method and a theorem of the authors and P. Shumyatsky about Lie rings with a metacyclic Frobenius group of automorphisms FH. It is also proved that G has a characteristic subgroup of (jCG(F)j; jFj)-bounded index whose order and rank are bounded in terms of jHj and the order and rank of CG(H), respectively, and whose exponent is bounded in terms of the exponent of CG(H)

    Finite groups and Lie rings with an automorphism of order 2n2^n

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    Suppose that a finite group GG admits an automorphism φ\varphi of order 2n2^n such that the fixed-point subgroup CG(φ2n1)C_G(\varphi ^{2^{n-1}}) of the involution φ2n1\varphi ^{2^{n-1}} is nilpotent of class cc. Let m=CG(φ)m=|C_G(\varphi)| be the number of fixed points of φ\varphi. It is proved that GG has a characteristic soluble subgroup of derived length bounded in terms of n,cn,c whose index is bounded in terms of m,n,cm,n,c. A similar result is also proved for Lie rings.Comment: minor corrections and addition

    Locally finite groups containing a 22-element with Chernikov centralizer

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    Suppose that a locally finite group GG has a 22-element gg with Chernikov centralizer. It is proved that if the involution in g\langle g\rangle has nilpotent centralizer, then GG has a soluble subgroup of finite index

    Finite groups and Lie rings with an automorphism of order 2n

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    Abstract. Suppose that a finite group G admits an automorphism ϕ of order 2n such that the fixed-point subgroup CG (ϕ2n−1) of the involution ϕ2n−1 is nilpotent of class c. Let m = |CG (ϕ)| be the number of fixed points of ϕ. It is proved that G has a characteristic soluble subgroup of derived length bounded in terms of n, c whose index is bounded in terms of m, n, c. A similar result is also proved for Lie rings

    Frobenius groups of automorphisms and their fixed points

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    Suppose that a finite group GG admits a Frobenius group of automorphisms FHFH with kernel FF and complement HH such that the fixed-point subgroup of FF is trivial: CG(F)=1C_G(F)=1. In this situation various properties of GG are shown to be close to the corresponding properties of CG(H)C_G(H). By using Clifford's theorem it is proved that the order G|G| is bounded in terms of H|H| and CG(H)|C_G(H)|, the rank of GG is bounded in terms of H|H| and the rank of CG(H)C_G(H), and that GG is nilpotent if CG(H)C_G(H) is nilpotent. Lie ring methods are used for bounding the exponent and the nilpotency class of GG in the case of metacyclic FHFH. The exponent of GG is bounded in terms of FH|FH| and the exponent of CG(H)C_G(H) by using Lazard's Lie algebra associated with the Jennings--Zassenhaus filtration and its connection with powerful subgroups. The nilpotency class of GG is bounded in terms of H|H| and the nilpotency class of CG(H)C_G(H) by considering Lie rings with a finite cyclic grading satisfying a certain `selective nilpotency' condition. The latter technique also yields similar results bounding the nilpotency class of Lie rings and algebras with a metacyclic Frobenius group of automorphisms, with corollaries for connected Lie groups and torsion-free locally nilpotent groups with such groups of automorphisms. Examples show that such nilpotency results are no longer true for non-metacyclic Frobenius groups of automorphisms.Comment: 31 page

    Statistical Analysis of Simulated Supernova Remnants in Optical Band

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    При вспышке сверхновой (СН) в межзвездную среду (МЗС) высвобождается около 1051 эрг. На поздних стадиях эволюции СН, около 70 % этой энергии теряется за счет радиационного охлаждения. Эти потери можно наблюдать в запрещенных оптических линиях. В данной работе мы провели статистическое исследование оптического излучения остатков СН, которые были смоделированы 3D-(магнито)гидродинамическим (МГД) кодом FLASH в реалистичной МЗС. Были рассмотрены два положения вспышки СН: на расстояниях 25 и 50 пк от центра масс молекулярного облака. В результате было выявлено, что наличие или отсутствие магнитного поля почти не влияет на оптическое излучение от СН. Однако распределение плотности в месте вспышки СН меняет всю дальнейшую эволюцию остатка СН. Это необходимо учитывать при сравнении моделей остатков СН и реальных наблюдений.During the supernova (SN) explosion, about 1051 erg is released into the interstellar medium (ISM). In the later stages of SN evolution, about 70 % of this energy is lost due to radiative cooling. This loss can be observed in forbidden lines in the optical range. In this work, we have carried out a statistical study of the optical emission of SN remnants, which are simulated using the 3D (magneto)hydrodynamic code FLASH in a realistic ISM. Two positions of the SN were considered: at distances of 25 and 50 pc from the centre of mass of the molecular cloud. As a result, the presence or absence of magnetic field has almost no effect on the optical radiation from the SN remnant. However, the density distribution at the site of the SN changes the entire evolution of the SN remnant. This should be taken into account when comparing simulations of SN remnants and real observations

    The experimental prophylaxis of the peroxide periodontitis by antidysbiotic means

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    Aim: To determine the periodontoprotective properties of antidysbiotic means (ADM) at the peroxide periodontitis.Methods: ADM (quertulyn, lequin, lecasil and lysozyme-forte) were used. The peroxide periodontitis was reproduced by peroxide sunflower oil introduction in during 2,5 month. The levels of MDA, elastase, urease, lysozyme, catalase were determined into gum. The levels of alkaline and acid phosphatase, calcium and protein were determined into periodontal bone.Results: The introduction of ADM the reduced the levels of inflammation markers (MDA and elastase) and to the degree of  dysbiosis but raised the levels of lysozyme and catalase into gum. ADM reduced the acid phosphatase activity but raised the alkaline phosphatase into bone.Conclusion: Lequin was more effective means as antiinflammation, quertulyn was more effective means as antidysbiotic action, lysozyme-forte was more effective means mineralization action. The lecitine contents means lequin and lecasil possessed more effective action on the degree mineralization of periodontal bone

    New IGIP Curriculum for Advanced Training of Engineering University Teachers

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    The discussion of the new Curriculum for pedagogical training of teachers of technical disciplines, prior to its approval by the IGIP Executive Committee in the fall of 2019 is considered. The previous version of this Curriculum was approved in 2013. Over the past period, there have been significant changes in the use of ICT in training, discussed in the proposals of the National IGIP Offices, in the proceedings of the Annual IGIP Conferences, including the International Conference ICL-IGIP held in Tallinn on 23–25 September, 2020. At this Conference, IGIP President Hanno Hortsch in his presentation has published the IGIP curriculum in the form of a table (now we present it in translation into Russian) and reported about his vision of its use. The authors formulate their point of view on the topic basing on the overview of the presentations given at this Conference and relevant articles published in the latest issues of the journal “Higher education in Russia”

    Preoperative donor zones preparation of perforant flaps by training perforant vessels with negative pressure

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    One of the key factors in achieving favorable treatment outcomes when planning reconstructive surgeries using perforant flaps is the choice of recipient vessels. Their identification causes certain difficulties both at the planning stage and during the operation. The aim of the study was to develop the most rational modes of action of negative pressure on the skin of the thigh. For preoperative preparation of the donor zone for the formation of perforant flaps, a local vacuum (VAC - action) was used, which was created using a negative pressure apparatus "AGAT-Dnepr" (Ukraine) by applying it to the anterior surface of the thigh. Preoperative location of perforants was performed using a Flir ONE (USA) thermal imager for smartphones and tablets based on Android. The studies were carried out on a group of healthy volunteers - 35 people: 17 women and 18 men aged 19 to 50 years on the basis of the burn department of the clinic in Dnipro, Ukraine in 2020-21. at the same time at the specified time intervals - 60 seconds (immediately after the action of negative pressure); 20, 30, 60 minutes; after 24 and 48 hours. The highest average number of perforants in the examined patients was observed after 30 minutes of VAC- action - 12.0 (6.0; 12.0), which was statistically significantly higher compared to their number, which was detected after 10 minutes of negative pressure action (p<0.001 ). On average, according to the median values of 12 perforants after 30 minutes, the VAC action remained after 20, 30 and 60 minutes and decreased only after 24 hours. Doubling the period of VAC - action to 60 minutes and no longer led to an increase in the number of perforators. Therefore, the optimal negative pressure time was 30 minutes when up to 10-12 perforants are opened. The smallest average number of perforants was observed at the pressure level P=(-100 mmHg) 24 hours after the VAC-action and at P=(-160 mmHg) 48 hours later. The largest average number of perforants was detected at the pressure level Р= (-130 mmHg) – 10.0 (8.0; 14.0), which was statistically significantly higher compared to their number under the negative impact of pressure Р =(-100 mmHg) (p<0.001). The indicator was constant, the number of perforators was maintained during the entire observation period from 30 minutes to 48 hours. The action of local negative pressure contributed to the opening of perforants of the second and third levels and thus improved blood supply to the donor area. Pressure Р= (-130 mm Hg) and time of 30 minutes was the most optimal mode of action on the skin of the anterior surface of the thigh, since 10 to 14 perforants were determined. The use of local negative pressure against the background of cooling may be useful for "training" the perforant vessels of the donor site for 2-3 days before surgery to reduce postoperative complications

    Synthesis and structure of 1-bromo-1-nitro-2-piperidino-(cyclohexylamino)-2-phenylethenes

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    A preparation method was developed for new representatives of halonitroenamines, 1-bromo-1-nitro-2-piperidino(cyclohexylamino)-2-phenylethenes. Both molecules possess E configuration and are of high polarity
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