Finite Abelian Group of | A(G) |= 27pq

we have discussed structures of Abelian group G by order |A(G) |of automoorphism group and have obtained all types of finite Abelian grooup G when the order of A(G) equals 27pq(p,q are odd primmes).

A Characterization of Metahomomorphisms on Abelian Groups

In this paper, a characterization of metahomomorphisms on Abelian groups is given.

THE SYSTEMS WITH ALMOST BANACH-MEAN EQUICONTINUITY FOR ABELIAN GROUP ACTIONS

In this paper,we present the concept of Banach-mean equicontinuity and prove that the Banach-,Weyl-and Besicovitch-mean equicontinuities of a dynamic system of Abelian group action are equivalent.Furthermore,we obtain that the topological entropy of a transitive,almost Banach-mean equicontinuous dynamical system of Abelian group action is zero.As an application of our main result,we show that the topological entropy of the Banach-mean equicontinuous system under the action of an Abelian groups is zero.

AN HARMONIC ANALYSIS FOR OPERATORS IN THE CASE OF A LOCALLY COMPACT ABELIAN GROUP：F．AND M．RIESZ THEOREMS

Let G be a locally compact Abelian group, B a homogeneous Banach algebra without the order on G. at denotes the set of all integrable operators with respect to right translation on B(see [2]). Under some convenient conditions we obtain the following results:both the first F. and M. Riesz Theorem for operators in and the second F. and M. Riesz Theorem for operators in hold.

Non-Full Rank Factorization of Finite Abelian Groups

Tilings of p-groups are closely associated with error-correcting codes. In [1], M. Dinitz, attempting to generalize full-rank tilings of ?Zn2??to arbitrary finite abelian groups, was able to show that if p ≥5, then?Znp? admits full-rank tiling and left the case p=3, as an open question. The result proved in this paper the settles of the question for the case p=3.

Splitting Extensions of Abelian by Hyper-(cyclic or finite) Groups (Ⅱ)

Let F be a locally defined formation consisting of locally solvable groups, G a hyper-（ cyclic or finite） locally solvable group and A a noetherian ZG-module with all irreducible ZG-factors being finite. The following conclusion is obtained： if G∈F, f（ ∞ ） include f（p）, f（p） ≠φ for each p∈π, and A has no nonzero F central ZG- images, then any extension E of A by G splits conjugately over A, and A has no nonzero F central ZG-factors.

An Application of Cyclotomic Polynomial to Factorization of Abelian Groups

If a finite abelian group G is a direct product of its subsets such that G = A1···Ai···An, G is said to have the Hajos-n-proprty if it follows that one of these subsets, say Ai is periodic, meaning that there exists a nonidentity element g in G such that gAi = Ai . Using some properties of cyclotomic polynomials, we will show that the cyclic groups of orders pα and groups of type (p2,q2) and (pα,pβ) where p and q are distinct primes and α, β integers ≥ 1 have this property.

Canonical Differential Calculi for Finitely Generated Abelian Groups and Their Fermionic Representations

Canonical differential calculi are defined for finitely generated Abelian groups with involutions existing consistently. Two such the canonical calculi are presented. Fermionic representations for canonical calculi are defined based on quantized calculi. Fermionic representations for aforementioned two canonical calculi are searched out.

Dynamical Properties of Additive Cellular Automata over Finite Abelian Groups

Some dynamical properties were discussed for additive cellular automata(CA)over finite abelian groups.These properties include surjection,ergodicity,sensitivity to initial conditions and positive expansivity.Some necessary and sufficient conditions of determining ergodicity and sensitivity of the above additive CA were presented,respectively.A necessary condition for the positive expansivity of the above additive CA was given.The positive expansivity was proved to be preserved under the shift mappings for the general CA.The discussion was mainly based on the structure theorem of the finite abelian groups and the matrix associated with the global rule of the additive CA over the finite abelian p-groups.

CALCULATION OF THE GIBBS DERIVATIVES ON FINITE ABELIAN GROUPS THROUGH THE DECISION DIAGRAMS

Paper considers the calculation of the values of Gibbs derivatives on finite Abelian groups. The calculation procedure is based upon the decision diagram representation of functions defined on finite Abelian groups. Approach permits processing of large functions.

A New Characterization of Simple K_3-groups

In this paper, We show that the simple K\-3-groups can be characterized by the orders of their maximal abelian subgroups. That is, we have Theorem Let G be a finite group and M a simple K \-3-group. Then G is isomorphic to M if and only if the set of the orders of the maximal abelian subgoups of G is the same as that of M .

A Note on Abelian Extensions

Let K/Q be any abelian extension where Q is the field of rational numbers. By Galois theory and the Frobenius formula for induced characters, we prove that there exists a metabelian group G and an irreducible character X of G such that K=Q（X）.

有限阶Abelian群同构类的计算

该文通过运用组合数学中整数分拆的知识,结合有限Abelian群的基本结构定理,给出了有限阶Abelian群的同构类的计算公式,使得对于所给的任意有限阶Abelian群,都可以通过该公式计算出它的同构群的种类,最后,作者把该方法在计算机上实现,尤其是当阶数取得很大并且已超越人脑计算时,这将使计算更加容易和便利.

Torsion in Groups of Integral Triangles

Let 0<γ<π be a fixed pythagorean angle. We study the abelian group Hr of primitive integral triangles (a,b,c) for which the angle opposite side c is γ. Addition in Hr is defined by adding the angles β opposite side b and modding out by π-γ. The only Hr for which the structure is known is Hπ/2, which is free abelian. We prove that for generalγ, Hr has an element of order two iff 2(1- cosγ) is a rational square, and it has elements of order three iff the cubic (2cosγ)x3-3x2+1=0 has a rational solution 0<x<1. This shows that the set of values ofγ for which Hr has two-torsion is dense in [0, π], and similarly for three-torsion. We also show that there is at most one copy of either Z2 or Z3 in Hr. Finally, we give some examples of higher order torsion elements in Hr.

Weak Isomorphism of Finite Group

On the basis of the quasi-isomorphism of finite groups, a new mapping, weak isomorphism, from a finite group to another finite group is defined. Let G and H be two finite groups and G be weak-isomorphic to H. Then G≌H if G satisfies one of the following conditions. 1） G is a finite Abelian group. 2） The order of G is p^3. 3 ） The order of G is p^n＋1 and G has a cyclic normal subgroup N = 〈a〉 of order p^n. 4） G is a nilpotent group and if p^││G│, then for any P ∈ Sylp （G）, P has a cyclic maximal subgroup, where p is a prime; 5） G is a maximal class group of order p4（p〉3）.

On Weakly Semi-radicable Groups

In this paper, we prove that if a torsion nilpotent group G is a weak semi-radicable group, then every Sylow p-group Gp is a central-by-finite p-group, and moreover Gp's center ζ(GP) satisfies |ζ(GP) : (ζ(GP))P| <∞, that is, ζ(GP) = D×F, where D is a divisible Abelian group, and F is a finite Abelian group.

Full-Rank Factoring of Elementary 2-Groups with Equal Size Factors

In order to answer a question motivated by constructing substitution boxes in block ciphers we will exhibit an infinite family of full-rank factorizations of elementary 2-groups into two factors having equal sizes.

Co-Periodicity Isomorphisms between Forests of Finite <I>p</I>-Groups

Based on a general theory of descendant trees of finite p-groups and the virtual periodicity isomorphisms between the branches of a coclass subtree, the behavior of algebraic invariants of the tree vertices and their automorphism groups under these isomorphisms is described with simple transformation laws. For the tree of finite 3-groups with elementary bicyclic commutator qu-otient, the information content of each coclass subtree with metabelian main-line is shown to be finite. As a striking novelty in this paper, evidence is provided of co-periodicity isomorphisms between coclass forests which reduce the information content of the entire metabelian skeleton and a significant part of non-metabelian vertices to a finite amount of data.

The Zero-divisor Graphs of Abelian Regular Rings

We introduce the zero-divisor graph for an abelian regular ring and show that if R,S are abelian regular, then (K0(R),[R])≌(K0(S),[S]) if and only if they have isomorphic reduced zero-divisor graphs. It is shown that the maximal right quotient ring of a potent semiprimitive normal ring is abelian regular, moreover, the zero-divisor graph of such a ring is studied.

Hajós-Property for Direct Product of Groups

We study decomposition of finite Abelian groups into subsets and show by examples a negative answer to the question of whether Hajós-property is inherited by direct product of groups which have Hajós-property.