The Firstly Discovered Cosmic Spherules in Carbonaceous Siltstone from the Taizi Formation of the Mesoproterozoic Shennongjia Group,Central China

Objective Spherical micro-particles are often preserved in Precambrian sedimentary rocks. Finnish and Chinese scholars have previously discovered carbonaceous, siliceous or ferruginous spherules of out-space origin in the 1.6 Ga and 1.4 Ga sequence, respectively. The presence of spherules can record possible cosmic impact events. Also, cosmic spherules provide important information on the evolution of planets from outer space.

China(Fujian)Foreign Trade Central Group

Subordinated to the Ministry of Foreign Trade and Economic Cooperation, the China (Fujian) Foreign Trade Central Group is a comprehensive foreign trade corporation engaging in imports and exports, real estate, international goods transportation, restaurants, advertising, exhibition

Centrally clean elements and central Drazin inverses in a ring

Element a in ring R is called centrally clean if it is the sum of central idempotent e and unit u.Moreover,a=e+u is called a centrally clean decomposition of a and R is called a centrally clean ring if every element of R is centrally clean.First,some characterizations of centrally clean elements are given.Furthermore,some properties of centrally clean rings,as well as the necessary and sufficient conditions for R to be a centrally clean ring are investigated.Centrally clean rings are closely related to the central Drazin inverses.Then,in terms of centrally clean decomposition,the necessary and sufficient conditions for the existence of central Drazin inverses are presented.Moreover,the central cleanness of special rings,such as corner rings,the ring of formal power series over ring R,and a direct product ∏ R_(α) of ring R_(α),is analyzed.Furthermore,the central group invertibility of combinations of two central idempotents in the algebra over a field is investigated.Finally,as an application,an example that lists all invertible,central group invertible,group invertible,central Drazin invertible elements,and centrally clean elements of the group ring Z_(2)S_(3) is given.

Transversality on locally pseudocompact groups

Two non-discrete Hausdorff group topologiesτandδon a group G are called transversal if the least upper boundτ⋁δofτandδis the discrete topology.In this paper,we discuss the existence of transversal group topologies on locally pseudocompact,locally precompact,or locally compact groups.We prove that each locally pseudocompact,connected topological group satisfies central subgroup paradigm,which gives an affirmative answer to a problem posed by Dikranjan,Tkachenko,and Yaschenko[Topology Appl.,2006,153:3338–3354].For a compact normal subgroup K of a locally compact totally disconnected group G,if G admits a transversal group topology,then G/K admits a transversal group topology,which gives a partial answer again to a problem posed by Dikranjan,Tkachenko,and Yaschenko in 2006.Moreover,we characterize some classes of locally compact groups that admit transversal group topologies.

Bogomolov Multipliers for Some p-groups of Nilpotency Class 2

The Bogomolov multiplier B0 （G） of a finite group G is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of G. The triviality of the Bogomolov multiplier is an obstruction to Noether＇s problem. We show that if G is a central product of G1 and G2, regarding Ki ≤ Z（Gi）,i = 1,2, and θ ： G1 →G2 is a group homomorphism such that its restriction θ｜K1 ： K1 → K2 is an isomorphism, then the triviality of Bo（G1/K1）, Bo（G1） and B0（G2） implies the triviality of Bo（G）. We give a positive answer to Noether＇s problem for all 2-generator p-groups of nilpotency class 2, and for one series of 4-generator p-groups of nilpotency class 2 （with the usual requirement for the roots of unity）.