On the Group of Reduced Identities of Relatively Free Solvable Groups

We prove that the groups of reduced identities of a free solvable group and a free metabelian group of a given nilpotency class are trivial whenever these groups are finitely generated.     

Locally Finite-Indicable Groups

A group is locally ?-indicable if every finitely generated subgroup has a nontrivial homomorphism onto a nontrivial ?-group. If ? is a quasi-variety, then the class L(?) of locally ?-indicable groups coincides with the class N(?) of groups which have normal systems with factors in ?. It is not known if ? must be a quasi-variety in order for the equality L(?) = N(?) to hold. We show here that if ? is the class of all finite groups, which is the union of an ascending sequence of quasi-varieties, then L(?) ≠ N(?). Examples of finitely generated groups in L(?)\ N(?) are also constructed.     

Structure of Quasi-Layer-Finite Groups

A group is said to be layer-finite if it has at most finitely many elements of any given order. In this paper, the structure of infinite groups all of whose proper subgroups are layer-finite is investigated.     

Continuous Selections and Locally Pseudocompact Groups

We characterize locally pseudocompact groups by means of the selection theory. Our result is the selection version of the well-known Comfort—Ross theorem on pseudocompactness which states that a topological group is pseudocompact if and only its Stone—Čech compactification is a topological group.     

PO_n的局部极大幂等元生成的子半群

研究了有限链上的部分保序变换半群PO_n.通过对其幂等元的分析,获得了PO_n的局部极大幂等元生成的子半群的结构与分类.     

Locally Finite Barely Transitive Groups

Infinite transitive permutation groups all proper subgroups of which have just finite orbits are treated. Under the extra condition of being locally finite, such groups are proved to be primary, and, moreover, soluble if the stabilizer of some point is soluble.     

Z_n分次代数的Hochschild上同调群

本文给出了Z_n分次代数A的Hochschild上同调群的定义,对低阶Hochschild上同调群进行了刻画.利用第一阶Hochschild上同调群给出了Z_n分次代数为分次可分代数的充要条件,证明了第二阶Hochschild上同调群的零次分支与A的Hochschild扩张之间的一一对应关系.     

Prym Representations of Mapping Class Groups

Let S be a closed orientable surface of genus at least 2 and let to S be a connected finite abelian covering with covering group $G$. The lifts of liftable mapping classes of S determine a central extension (by G) of a subgroup of finite index of the mapping class group of S. This extension acts on H₁( ). With a few exceptions for genus 2, we determine the Zariski closure of the image of this representation, and prove that the image is an arithmetic group.     

Power Semigroups of a Class of Cliford Semigroups

Let S =∪(Gα : α∈ E) be a semilattice of groups(i.e., a Cliford semigroup) and n a natural number. E is called an n-element chain of groups if it is an n-element chain. Denote by Cn the set of all n-element chains of groups. In this paper we shall show that for any natural number n, the class of semigroups Cn satisfies the strong isomorphism property.     

Groups Saturated by a Finite Set of Groups

We study the periodic groups that are saturated by a finite set of finite (nonabelian simple) groups, obtaining some information about the elements of the saturating set.     

Pontryagin Duality for a Class of Locally Compact Quantum Groups

A class of locally compact quantum semigroups in the sense of WORONOWICZ , containing the quantized Heisenberg group, is studied. The underlying quantum space is described in terms of a crossed product. We show the existence of a universal corepresentation and a Pontryagin dual, which turns out to be a twisted crossed product. The Pontryagin duality for these quantum semigroups is investigated.     

Mapping Class Groups of Hyperbolic Surfaces and Automorphism Groups of Graphs

Let M be a hyperbolic surface and (M) its extended mapping class group. We show that (M) is isomorphic to the automorphism group of the following graph G(M). The set of vertices of G(M) is the set S(M) of nonseparating simple closed geodesics of M. Two vertices u and v of S(M) are related by an edge if u and v intersect exactly once in M. The graph G(M) can be thought of as a combinatorial model for M.     

Finite Sylow Subgroups in Simple Locally Finite Groups of Lie Type

The main result of the paper is the followingTheorem. Let S = {r₀, r₁, ..., r_n} be a finite nonempty set of primes and let L be a Lie type of Chevalley groups. Then there exists a locally finite field F of characteristic r₀ such that Sylow r-subgroups of the simple group L(F) of type L over F are finite if and only if r ? S.     

Boundeness of a Class of Maximal Operators on H~p Spaces on Compact Lie Groups

In this paper we discuss the weak type(H^p,L^p) boundedness of a class of maximal operators T*^ψ and themaximal strong mean boundedness of a family of the operators ｛T^ψ｝ on the atomic H^p spaces on compact Lic groups.Also,we obtain the correspoding convergent results.     

Vilenkin群上的加权Hardy空间中的乘子

本文主要研究了Vilenkin群上的加权Hardy空间的原子分解,证明了一个加权H^p乘子定理并给出其应用。     

The Class Number of Derived Subgroups and the Structure of Camina Groups

A finite group G is called a Camina group if G has a proper normal subgroup N such that gN is precisely a conjugacy class of G for any g ∈E G - N. In this paper, the structure of a Camina group G is determined when N is a union of 2, 3 or 4 conjugacy classes of G.     

Locally maximal idempotent-generated subsemigroups of singular orientation-preserving transformation semigroups

In this paper we study locally maximal idempotent-generated subsemigroups of finite singular orientation-preserving transformation semigroups. This work is supported by N.S.F. and E.S.F. of Guizhou.