The Gruenberg-Kegel graph(or the prime graph)Γ(G)of a finite group G is a graph,in which the vertex set is the set of all prime divisors of the order of G and two different vertices p and q are adjacent if and only i...The Gruenberg-Kegel graph(or the prime graph)Γ(G)of a finite group G is a graph,in which the vertex set is the set of all prime divisors of the order of G and two different vertices p and q are adjacent if and only if there exists an element of order pq in G.The paw is a graph on four vertices whose degrees are 1,2,2,3.We consider the problem of describing finite groups whose Gruenberg-Kegel graphs are isomorphic as abstract graphs to the paw.For example,the Gruenberg-Kegel graph of the alternating group A_(10)of degree 10 is isomorphic as abstract graph to the paw.In this paper,we describe finite non-solvable groups G whose Gruenberg-Kegel graphs are isomorphic as abstract graphs to the paw in the case when G has no elements of order 6 or the vertex of degree 1 ofΓ(G)divides the order of the solvable radical of G.展开更多
The Russian Far East is a region between China and the Russian Arctic with a diverse climatological,geophysical,oceanic,and economical characteristic.The southern region is located in the Far East monsoon sector,while...The Russian Far East is a region between China and the Russian Arctic with a diverse climatological,geophysical,oceanic,and economical characteristic.The southern region is located in the Far East monsoon sector,while the northern parts are affected by the Arctic Ocean and cold air masses penetrating far to the south.Growing economic activities and traffic connected to the China Belt and Road Initiative together with climate change are placing an increased pressure upon the Russian Far East environment.There is an urgent need to improve the capacity to measure the atmospheric and environmental pollution and analyze their sources and to quantify the relative roles of local and transported pollution emissions in the region.In the paper,we characterize the current environmental and socio-economical landscape of the Russian Far East and summarize the future climate scenarios and identify the key regional research questions.We discuss the research infrastructure concept,which is needed to answer the identified research questions.The integrated observations,filling in the critical observational gap at the Northern Eurasian context,are required to provide state-of-the-art observations and enable follow-up procedures that support local,regional,and global decision making in the environmental context.展开更多
基金supported by the Russian Science Foundation(project 19-71-10067).
文摘The Gruenberg-Kegel graph(or the prime graph)Γ(G)of a finite group G is a graph,in which the vertex set is the set of all prime divisors of the order of G and two different vertices p and q are adjacent if and only if there exists an element of order pq in G.The paw is a graph on four vertices whose degrees are 1,2,2,3.We consider the problem of describing finite groups whose Gruenberg-Kegel graphs are isomorphic as abstract graphs to the paw.For example,the Gruenberg-Kegel graph of the alternating group A_(10)of degree 10 is isomorphic as abstract graph to the paw.In this paper,we describe finite non-solvable groups G whose Gruenberg-Kegel graphs are isomorphic as abstract graphs to the paw in the case when G has no elements of order 6 or the vertex of degree 1 ofΓ(G)divides the order of the solvable radical of G.
基金Research of the first author is supported by a NNSF grant of China(Grant No.11371335)Wu Wen-Tsun Key Laboratory of Mathematics of Chinese Academy of Science.The second author was supported by the Russian Foundation for Basic Research(Project No.13-01-00469)+1 种基金the Complex Program of UB RAS(Project 15-16-1-5)under the Agreement 02.A03.21.0006 of 27.08.2013 between the Ministry of Education and Science of the Russian Federation and Ural Federal University.
文摘In this paper,we determine the finite minimal non-supersolvable groups decomposable into the product of two normal supersolvable subgroups.
基金supported by RFBR project[18-05-60219](РоссийскийФондФундаментальныхИсследований(РФФИ))The work was funded by Academy of Finland[307537,333397,334792]+1 种基金Belmont Forum(through Academy of Finland project 334792)University of Helsinki.
文摘The Russian Far East is a region between China and the Russian Arctic with a diverse climatological,geophysical,oceanic,and economical characteristic.The southern region is located in the Far East monsoon sector,while the northern parts are affected by the Arctic Ocean and cold air masses penetrating far to the south.Growing economic activities and traffic connected to the China Belt and Road Initiative together with climate change are placing an increased pressure upon the Russian Far East environment.There is an urgent need to improve the capacity to measure the atmospheric and environmental pollution and analyze their sources and to quantify the relative roles of local and transported pollution emissions in the region.In the paper,we characterize the current environmental and socio-economical landscape of the Russian Far East and summarize the future climate scenarios and identify the key regional research questions.We discuss the research infrastructure concept,which is needed to answer the identified research questions.The integrated observations,filling in the critical observational gap at the Northern Eurasian context,are required to provide state-of-the-art observations and enable follow-up procedures that support local,regional,and global decision making in the environmental context.
