A Note on Invariants Over Finite Local Rings

In this note, we prove a conjecture of Steinberg [10 Steinberg , R. (1987). On Dickson's theorem on invariants. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34:699–707. [Google Scholar]] about modular invariants of some linear groups over finite commutative local rings.     

Strongly Modular Subgroup in Finite Group

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A Note on Characterizing the k-OPTNeighborhood Via Group Theory

Group theory can be used to model and synthesize the neighborhood of Traveling Salesman tours reachable through k-OPT exchanges. A primary concept is that a dihedral group action partitions the sets of cut arcs so that k-OPT exchanges of orbital elements are conjugate. Also presented is a method to produce all k-OPT exchanges for a given set of cut arcs.     

A Note on Periodicity in Representation Theory of Finite Dimensional Algebras

Let Λ be an algebra over an algebraically closed field K of infinite transcendence degree over its prime subfield. We prove in particular that if every s-dimensional indecomposable nonprojective Λ-module is Ω-periodic (resp. DTr-periodic) then there exists a common bound for the Ω-periods (resp. DTr-periods) of s-dimensional indecomposable nonprojective Λ-modules.     

关于有限群表示范畴上几乎可裂序列的注记(英文)

本文给出几乎可裂序列的Green对应.主要结果为:设X是不可分解非投射kG-模,Y是相应的不可分解非投射kL-模,那么(i)0→Ω~2(X)→(XU)_0→X→0是可裂正和列当且仅当0→Ω~2(Y)→(YU)_0→Y→0是可裂正和列;(ⅱ)0→Ω~2(X)→(X(U)_0→X→0是几乎可裂正和列当且仅当0→Ω~2(Y)→(YU)_0→Y→0是几乎可裂正和列.     

模特征标度图

本文假设G为一有限群且G的模特征标度图有两个连通分支。记πi(i=1,2)为其顶点集。文章通过p-长界定了G的πi-长，并证明了G的π1－或π2－长至多为4。     

有限超特殊p-群的一个注记

本文获得了以下结果：设G为有限超特殊P-群．则下列条件等价：（1）G的非平凡特征子群的阶相同；（2）G的非平凡特征子群唯一；（3）当p〉2时，exp G=p；当P=2时，G≠D8．     

A Note on Semilocal Group Rings

Let R be an associative ring with identity and let J(R) denote the Jacobson radical of R. R is said to be semilocal if R/J(R) is Artinian. In this paper we give necessary and sufficient conditions for the group ring RG, where G is an abelian group, to be semilocal.     

A Note on the Range of Toeplitz Operators

A well known lemma attributed to Coburn states that a Toeplitz operator with non-trivial kernel acting on the Hardy space must have dense range. We show that the range of a non-zero Toeplitz operator with non-trivial kernel must contain all polynomials and state this in a precise form.     

关于CAP-子群的一点注记（英文）

对于有限群G的每一主因子H/K来说,若G的子群L满足LH=LK或者L∩H=L∩K,则称L是G的CAP-子群.本文通过假设G的每个非循环Sylow子群P有一个子群D使得1〈｜D｜〈｜P｜,且P的所有阶为｜D｜和2｜D｜（若P是非交换2-群且｜P∶D｜〉2）的子群H是G的CAP-子群,得到G为p-幂零群的一个结果.     

A Note on the Spectrum of Invertible p-hyponormal Operators

A bounded linear operator T is clalled p-hyponormal if (T*T)^p ≥ (TT)^p, 0 < p < 1. It is known that for semi-hyponormal operators (p = 1/2), the spectrum of the operator is equal to the union of the spectra of the general polar symbols of the operator. In this paper we prove a somewhat weaker result for invertible p-hyponormal operators for 0 < p < 1/2.     

A Transcendence Basis in the Differential Field of Invariants of Pseudo-Galilean Group

Russian Mathematics - Let G be a subgroup in the group of all invertible linear transformations of a finite-dimensional real space X. One of the problems in differential geometry is that of finding...     

A Note on Almost Regular Group Rings

It is proved that a group ring R = AG is almost regular if and only if (i) the ring A is almost regular; (ii) the group G is locally finite; (iii) the order |H| of every finite subgroup H of G is invertible in A. Bibliography: 7 titles.     

A Note on Multiplicative Ideal Theory

We state a semigroup version of (19.15)THEOREM and (36.2)THEOREM, and disprove (30.9)THEOREM of Gilmers book [3] for commutative semigroups. We give a condition for the Kronecker function ring D* with respect to a star-operation * on an integral domain D to be well-defined.2000 Mathematics Subject Classification: Primary 13A15 Secondary 20M14.     

A Note on Euclidean Ramsey Theory

Suppose n ≥ 2 and are such that X is infinite and Y is the set of vertices of an n-simplex. Then there is blue/red coloring of such that no set similar to X is monochromatically blue and no set similar to Y is monochromatically red.     

A Note on *-paranormal Operators

In this note we show that if either T or T^* is totally *-paranormal then Weyls theorem holds for f(T) for every f , and also a-Weyls theorem holds for f(T) if T is totally *-paranormal. We prove that if either T or T^* is *-paranormal then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.     

A Note on Solitary Subgroups of Finite Groups

We say that a subgroup H of a finite group G is solitary (respectively, normal solitary) when it is a subgroup (respectively, normal subgroup) of G such that no other subgroup (respectively, normal subgroup) of G is isomorphic to H. A normal subgroup N of a group G is said to be quotient solitary when no other normal subgroup K of G gives a quotient isomorphic to G/N. We show some new results about lattice properties of these subgroups and their relation with classes of groups and present examples showing a negative answer to some questions about these subgroups.     

A Note on c-Supplemented Subgroups of Finite Groups

A subgroup H of a finite group G is said to be c-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K is contained in H _G , where H _G is the largest normal subgroup of G contained in H. In this article, we prove that G is solvable if every subgroup of prime odd order of G is c-supplemented in G. Moreover, we prove that G is solvable if and only if every Sylow subgroup of odd order of G is c-supplemented in G. These results improve and extend the classical results of Hall's articles of (1937) and the recent results of Ballester-Bolinches and Guo's article of (1999), Ballester-Bolinches et al.'s article of (2000), and Asaad and Ramadan's article of (2008).     

A Note About Critical Percolation on Finite Graphs

In this note we study the geometry of the largest component C₁\mathcal {C}_{1} of critical percolation on a finite graph G which satisfies the finite triangle condition, defined by Borgs et al. (Random Struct. Algorithms 27:137–184, 2005). There it is shown that this component is of size n ^2/3, and here we show that its diameter is n ^1/3 and that the simple random walk takes n steps to mix on it. By Borgs et al. (Ann. Probab. 33:1886–1944, 2005), our results apply to critical percolation on several high-dimensional finite graphs such as the finite torus \mathbbZ_n^d\mathbb{Z}_{n}^{d} (with d large and n→∞) and the Hamming cube {0,1} ⁿ .     

A Note on the Finite Element Method for the Reissner-Mindlin Plate

In this short note we use the idea of R.Duran [5] and introduce a new low-order triangular element by replacing the nonconforming linear element for the rotation in [2] with the conforming linear element.The optimal order error estimates are obtained uniformly in the plate thickness.