Crossed products for Hopf group-algebras

First,the group crossed product over the Hopf group-algebras is defined,and the necessary and sufficient conditions for the group crossed product to be a group algebra are given.The cleft extension theory of the Hopf group algebra is introduced,and it is proved that the crossed product of the Hopf group algebra is equivalent to the cleft extension.The necessary and sufficient conditions for the crossed product equivalence of two Hopf groups are then given.Finally,combined with the equivalence theory of the Hopf group crossed product and cleft extension,the group crossed product constructed by the general 2-cocycle as algebra is determined to be isomorphic to the group crossed product of the 2-cocycle with a convolutional invertible map of the 2-cocycle.The unit property of a general 2-cocycle is equivalent to the convolutional invertible map of the 2-cocycle,and the combination condition of the weak action is equivalent to the convolutional invertible map of the 2-cocycle and the combination condition of the weak action.Similarly,crossed product algebra constructed by the general 2-cocycle is isomorphic to the Hopfπ-crossed product algebra constructed by the 2-cocycle with a convolutional invertible map.

REVERSE ORDER LAW FOR GROUP INVERSE OF PRODUCT OF MATRICES ON SKEW FIELDS

Let Kn×n be the set of all n×n matrices and Krn×n the set {A∈Kn×n|rankA=r} on askew field K. Zhuang [1] denotes by A# the group inverse of A∈Kn×n which is the solu-tion of the euqations:AXA=A, XAX=X, AX=AX.

THE WREATH PRODUCT GROUP FOR NMR SPECTRA ANALYSES OF MOLECULA WITH S_4[S_2]SYMMETRY

This paper presents a character table of S_4 wr S_2 wreath product group.Using this character table,~1H or ^(13)C NMR spectra analysis of molecula with S_4[S_2]symmetry,especially simplification of the secular determinant equation will be easy to carry out. Molecules with S_4[S_2]symmetry,are exemplified by octaphenylcyclo- tetrasiloxane and 2,3,7,8,12,13,17,18-octaethyl-21H,23H-porphine chromium (Ⅲ)chloride.

A Restriction Theorem on the Reduced Product Heisenberg Group

In this paper,we give the Plancherel formula on the reduced product Heisenberg group,and obtain a restriction theorem on this group.

Representations of Free Groups on Rational Line Q

A.M.W. Glass and S.H.McCleary have given the 2 transitive representation of the countable free l group F η(1<η≤ω 0 ).In this paper we shall give the highly ordered transitive representation of countable free groups on the rational line Q, which generalizes their results. As applications,we obtain the highly ordered transitive representation for the direct product of countable free groups,and the inverse limit of countable free groups must be an action on the set Q.

Products of the Qingqi Motorcycle Group

The Qingqi Bamulan AG 100 has a streamlined body with super-low wind resistance and is modem in style. Its advanced two-stroke air-cooled motor is of high power, Stepless speed device enables it to be driven in a smooth and stable way. Fully functional meters are available to accurately represent all its working functions. Its high-performance damping system makes traveling comfortable. Its electrical starting device makes starting easy.

Cost Deployment Tool for Technological Innovation of World Class Manufacturing

This article brings a discussion about using the Cost Deployment methodology for technological innovation in the World Class Manufacturing (WCM) systems at Fiat Group Automobiles Production System (FAPS). It aims to show how this tool acts in the technical pillars of the WCM, and its proper use as an alternative to innovate in production processes, achieving a drastic reduction in wastes and cost optimization during specific activities in production systems. The Cost Deployment builds a distinctive transversal method of WCM which helps to promote and provide extremely effectiveness in the activation of more specific methods that have been tried successfully in the Japanese manufacturing improvements. It also allows to link the operational performances, usually measured with indicators such as efficiency, providing number of defects, hours of desaturation. The used methodology was based on a literature review about the proposed topic. It ends up finding that the Cost Deployment tool is one of the most sophisticated technological innovations existing for the production systems of the World Class Manufacturing.

Baise Mining Group's 300,000 t/a Aluminum Project Achieved Production Target, 10000 t/a High Purity Aluminum Project Broke Ground

The 10000 t/a high purity aluminum engineering project in Baise Mining Group’s Coal-power-aluminum Integration Project started construction at Tianyang Xinshan Aluminum Industrial Park.Following the successful production launching of Baise Mining Group’s Coal-power-aluminum Integration Xinshan Project-Phase I2×350MW coal-fired unit self supply

Factorizations of groups and related topics

This is a survey of some recent progress in the theory of groups with factorizations. Some of the methods can be used to obtain information about finite groups in general, nilpotent algebras and nearrings.

Convergence in L^p-norm of Fourier Series on the Complete Product of Quaternion Groups with Bounded Orders

A well-known result for Vilenkin systems is the fact that for all 1 〈 p 〈 oc the n-th partial sums of Fourier series of all functions in the space Lp converge to the function in LP-norm. This statement can not be generalized to any representative product system on the complete product of finite non-abelian groups, but even then it is true for the complete product of quaternion groups with bounded orders and monomial representative product system ordered in a specific way.

Factorizations of Finite Groups and Related Topics

This is a survey on the recent progress in the theory of finite groups with factorizations and around it,done by the author and his coauthors,and this has no pretensions to cover all topics in this wide area of research.In particular,we only touch the great consequences of the fundamental paper of Liebeck,Praeger and Saxl on maximal factorizations of almost simple finite groups for the theory of groups with factorizations.In each case the reader can find additional references at the end of Section 1.Some of the methods of investigation can be used to obtain information about finite groups in general,nilpotent algebras and related nearrings.

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）.

Tensor products of complementary series of rank one Lie groups

We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β)for small parameters α and β(in our parametrization). We prove further that for SO_0(n, 1) there are finitely many complementary series of the form π_(α+β+2j,)j = 0, 1,..., k, appearing in the tensor product π_α ? π_βof two complementary series π_α and π_β, where k = k(α, β, n) depends on α, β and n.