39 research outputs found
Frobenius groups of automorphisms and their fixed points
Suppose that a finite group admits a Frobenius group of automorphisms
with kernel and complement such that the fixed-point subgroup of
is trivial: . In this situation various properties of are
shown to be close to the corresponding properties of . By using
Clifford's theorem it is proved that the order is bounded in terms of
and , the rank of is bounded in terms of and the rank
of , and that is nilpotent if is nilpotent. Lie ring
methods are used for bounding the exponent and the nilpotency class of in
the case of metacyclic . The exponent of is bounded in terms of
and the exponent of by using Lazard's Lie algebra associated with the
Jennings--Zassenhaus filtration and its connection with powerful subgroups. The
nilpotency class of is bounded in terms of and the nilpotency class
of 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
Quadratic equations over free groups are NP-complete
We prove that the problems of deciding whether a quadratic equation over a
free group has a solution is NP-complete
A lattice in more than two Kac--Moody groups is arithmetic
Let be an irreducible lattice in a product of n infinite irreducible
complete Kac-Moody groups of simply laced type over finite fields. We show that
if n is at least 3, then each Kac-Moody groups is in fact a simple algebraic
group over a local field and is an arithmetic lattice. This relies on
the following alternative which is satisfied by any irreducible lattice
provided n is at least 2: either is an S-arithmetic (hence linear)
group, or it is not residually finite. In that case, it is even virtually
simple when the ground field is large enough.
More general CAT(0) groups are also considered throughout.Comment: Subsection 2.B was modified and an example was added ther
Клиническая эффективность и безопасность применения иммунной плазмы реконвалесцентов для лечения COVID-19
Aim: to evaluate the efficacy and safety of convalescent plasma therapy for patients with severe SARS-CoV-2 infection.Materials and methods: the study included 64 patients with laboratory-confirmed severe new coronavirus infection. The control group consisted of 58 patients who, in addition to standard therapy, received a transfusion of plasma from donors who had recovered from COVID-19. The effectiveness of immune plasma was assessed by the duration of fever, the level of oxygen (SpO2 %) in dynamics, the detection of SARSCoV-2 RNA in nasopharyngeal and oropharyngeal swabs using PCR method in dynamics, as well as by the dynamics of blood tests results. Adverse events (any medically adverse events that occurred after immune plasma transfusion) were recorded as safety criteria.Results: patients who received convalescent plasma, showed a significantly shorter period of SARS-CoV-2 replication compared with the control group. The use of immune plasma did not have a statistically significant effect on the duration of the fever, as well as the dynamics of blood oxygenation. Also, there were no significant differences compared with the control group when assessing blood tests parameters.Conclusion: The use of COVID-19 convalescent plasma to treat severe COVID-19 did not show significant clinical effect but reduced the period of viral replication. It also showed no unexpected or serious adverse events. Цель. Оценка эффективности и безопасности применения иммунной плазмы реконвалесцентов для лечения COVID-19 у пациентов с тяжелой степенью тяжести.Материалы и методы. В исследование были включены 64 пациента с подтвержденной новой коронавирусной инфекцией тяжёлой степени тяжести, которым, помимо стандартной терапии, проводили трансфузию иммунной плазмы реконвалесцентов новой коронавирусной инфекции. Контрольную группу составили 58 пациентов, получавших базисную терапию. Эффективность терапии иммунной плазмы оценивалась по длительности лихорадки, уровню сатурации (SpO2 %), выявлению РНК SARS-CoV-2 методом ПЦР в отделяемом со слизистой рото-/носоглотки в динамике, а также по изменениям общеклинических и биохимических показателей крови. В качестве критериев безопасности регистрировались нежелательные явления (любые неблагоприятные с медицинской точки зрения события, возникшие после трансфузии иммунной плазмы).Результаты. У пациентов, получавших иммунную плазму реконвалесцентов, отмечался достоверно более короткий период вирусной репликации SARS-CoV-2 по сравнению с контрольной группой. На продолжительность лихорадки, а также динамику насыщения кислородом крови применение иммунной плазмы статистически значимого влияния не оказывало. Также не отмечалось достоверных различий по сравнению с контрольной группой при оценке общеклинических, биохимических показателей крови.Заключение. Терапия пациентов с тяжёлым течением COVID-19 иммунной плазмой реконвалесцентов, перенёсших инфекцию, вызванную SARS-CoV-2, достоверно не оказывала значимого клинического эффекта, однако сокращала период репликации вируса. Трансфузия иммунной плазмы также не вызывала серьёзных нежелательных явлений