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

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

Suppose that a finite group $G$ admits an automorphism $\varphi$ of order $2^n$ such that the fixed-point subgroup $C_G(\varphi ^{2^{n-1}})$ of the involution $\varphi ^{2^{n-1}}$ is nilpotent of class $c$. Let $m=|C_G(\varphi)|$ be the number of fixed points of $\varphi$. 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.Comment: minor corrections and addition

Non-linear water waves generated by impulsive motion of submerged obstacles

A fully non-linear problem on unsteady water waves generated by an impulsively moving obstacle is studied analytically. Our method involves reduction of the Euler equations to the integral-differential system for the wave elevation together with normal and tangential fluid velocities at a free surface. Exact model equations are derived in explicit form in a case where an isolated obstacle is presented by a totally submerged elliptic cylinder. A small-time asymptotic solution is constructed for a cylinder which starts with constant acceleration from rest. It is demonstrated that the leading-order solution terms describe several wave regimes such as the formation of non-stationary splash jets by vertical rising or vertical submersion of the obstacle; the generation of diverging waves is also observed

ВИЗНАЧЕННЯ ОСНОВНИХ ДЕТЕРМІНАНТ ПОПИТУ НА МІЖНАРОДНІ РЕЗЕРВИ В УКРАЇНІ: КОІНТЕГРАЦІЙНИЙ АНАЛІЗ

In this paper we searched for the most important determinants of reserve holdings inUkraineusing quarterly data from 2000 to 2013 years. We evaluated their importance using two econometric techniques: autoregressive distributed lag (ARDL) approach and Vector Error Correction model (VECM) approach. We find that the ratio of imports to GDP, the ratio of broad money to GDP, ratio of net foreign direct investment to GDP, the ratio of short term debt to GDP and GDP determine Ukraine’s long-run reserves demand function. Our empirical results show that shocks associated with the financial account is more dangerous for the Ukrainian economy than current account shocks. The low speed of adjustment coefficient of error correction model suggests that National Bank ofUkrainehas to carry out more active reserve management policy. Results denied the precautionary motive of reserves accumulation over the long term.В статье с помощью двух эконометрических техник (построение векторной модели коррекции ошибок и построение авторегрессионной модели с распределенным лагом) выявлено наличие долгосрочной и краткосрочной связи и их направление между международными резервами и факторами, определяющими их динамику. К основным факторам, которые уменьшают резервы в долгосрочном периоде относятся рост склонности к импорту, рост спроса на деньги и размера краткосрочного долга по остаточному сроку погашения, тогда как рост объемов ВВП и чистого притока прямых иностранных инвестиций увеличивают резервы. Доказано, что шоки, связанные с финансовым счетом платежного баланса, являются более опасными для украинской экономики, чем шоки текущего счета платежного баланса.У даній статті за допомогою двох економетричних технік (побудова векторної моделі коригування помилки та побудова авторегресійної моделі з розподіленим лагом) виявлено наявність довгострокового та короткострокового зв’язку та його напрямок між міжнародними резервами та факторами, що визначають їх динаміку. Основними факторами, що зменшують резерви у довгостроковому періоді визначено зростання схильності до імпорту, зростання попиту на гроші та розміру короткострокового боргу за залишковим терміном погашення, тоді як збільшують резерви зростання обсягів ВВП та чистого припливу прямих іноземних інвестицій. Доведено, що шоки, пов’язані з фінансовим рахунком платіжного балансу, є більш загрозливими для української економіки, ніж шоки поточного рахунку

Locally finite groups containing a 22-element with Chernikov centralizer

Suppose that a locally finite group $G$ has a $2$-element $g$ with Chernikov centralizer. It is proved that if the involution in $\langle g\rangle$ has nilpotent centralizer, then $G$ has a soluble subgroup of finite index

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

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