一类中心循环的有限p-群的自同构群的研究

本文研究了一类中心循环的有限p-群G的自同构群.利用在G的导群上作用平凡的自同构以及环上的辛群和正交群,确定了G的自同构群的结构,这推广了Bornand的相应结果.     

多属性群决策算法及一致性分析研究

在多属性群决策中 ,集结群体意见之前必须先对群体的决策数据进行一致性分析 ,以确保群体作出的决策符合客观实际 .提出了群决策的三种三维层次模型 ;用欧几里得距离 ( Euclidean Distance)表示个人决策中方案的评价值 ;然后设置一致性指标值α,作为群体数据一致性的判断依据 ;提出了满足一致性基础上的一种群决策方法 ;最后用实例说明了算法的使用步骤 .     

A complex for right-angled Coxeter groups

We associate to each right-angled Coxeter group a 2-dimensional complex. Using this complex, we show that if the presentation graph of the group is planar, then the group has a subgroup of finite index which is a 3-manifold group (that is, the group is virtually a 3-manifold group). We also give an example of a right-angled Coxeter group which is not virtually a 3-manifold group.

     

A Gap Cohomology Group

Dan Talayco has recently defined the gap cohomology group of a tower in p(ω)/fin of height ω₁. This group is isomorphic to the collection of gaps in the tower modulo the equivalence relation given by two gaps being equivalent (cohomologous) if their levelwise symmetric difference is not a gap in the tower, the group operation being levelwise symmetric difference. Talayco showed that the size of this group is always at least 2^N0 and that it attains its greatest possible size, 2^N1, if ? holds and also in some generic extensions in which CH fails, for example on adding many Cohen or random reals. In this paper it is shown that there is always some tower whose gap cohomology group has size 2^N1. It is still open as to whether there are models in which there are towers whose gap cohomology group has size less than 2^ω1.     

有限群中素数方幂阶子群的个数

本文利用基础代数中有关稳定子、陪集等理论,给出了有限群G中pk阶子群个数的 一个结果.     

A New Characterization of A 22 by Its Spectrum

It is proved that a finite group whose element order set is the same as that of an alternating group A ₂₂ of degree 22 is isomorphic to A ₂₂.     

A Parametric Family of Intersective Polynomials with Galois Group A 4

We give an infinite family of intersective polynomials with Galois group A ₄, the alternating group on four letters.     

关于几乎拓扑群的注记

In this paper, we mainly discuss some generalized metric properties and the cardinal invariants of almost topological groups. We give a characterization for an almost topological group to be a topological group and show that:(1) Each almost topological group that is of countable π-character is submetrizable;(2) Each left λ-narrow almost topological group isλ-narrow;(3) Each separable almost topological group is ω-narrow. Some questions are posed.     

Zassenhaus猜想的一个注记

在这篇注记中,通过研究两个有限群直积的整群环的正规化挠单位的偏增广,证明了在某些条件下这些正规化挠单位与该群中的元素在有理群代数中共轭.     

A new uncountably categorical group

We construct an uncountably categorical group with a geometry that is not locally modular. It is not possible to interpret a field in this group. We show the group is CM-trivial.

     

A perfect non-topologizable group

The first example of a group G whose automorphism group Aut (G) admits only discrete separated topology is presented in the paper. The group G is isomorphic to Aut (G) and all elements of the group G except for the unity satisfy some equation w(x) = 1.     

A Sparse-Group Lasso

For high-dimensional supervised learning problems, often using problem-specific assumptions can lead to greater accuracy. For problems with grouped covariates, which are believed to have sparse effects both on a group and within group level, we introduce a regularized model for linear regression with ?₁ and ?₂ penalties. We discuss the sparsity and other regularization properties of the optimal fit for this model, and show that it has the desired effect of group-wise and within group sparsity. We propose an algorithm to fit the model via accelerated generalized gradient descent, and extend this model and algorithm to convex loss functions. We also demonstrate the efficacy of our model and the efficiency of our algorithm on simulated data. This article has online supplementary material.     

A Class of Coquasitriangular Hopf Group Algebras

This article is devoted to constructing a class of coquasitriangular Hopf group algebras. First, we introduce the notion of group unified product. Then we prove the classification theorem for group unified products and discuss the sufficient and necessary conditions to make the group unified product to be a coquasitriangular Hopf group-algebra. Finally, some applications of the main results are considered.     

有限群的一个类函数的模构造

本文研究了有限群上的一个类函数.通过计算它和不可约特征标的内积,证明了它是特征标并且通过复群代数的中心的正则表示给出了它的一个模构造.     

Dedekind 群的一个刻画

本文给出了Dedekind群的一个刻画.即如果一个群G有一个无不动点的弱幂同构,则G是一个Dedekind群.     

A finitary Tits' alternative

It is shown that for any family of finite groups of uniformly bounded rank, either (i) a subdirect product of these groups contains a non-cyclic free group, or (ii) there exists a single word w which is a law in each group, and moreover, if N is the length of the word, and r the maximal rank of each finite group, then each group is nilpotent-of-bounded class-by-abelian-by-bounded-index, with the bounds being functions of N and r alone. Additionally, various corollaries are derived from this result.     

A characterization of the determinant

In this paper we examine group morphisms Λ: GL_n(R) → R^* from the general linear group over a commutative ring R into the group of units R^* of R and ask, "When are these morphisms functions of the determinant?"     

A Polish group without Lie sums

We construct a Polish group with an invariant metric in which Lie sums and Lie brackets do not exist. The construction of the group and the proof of the main theorem use some facts of combinatorial nature about the free group with two generators equipped with a Graev metric. The second author acknowledges the United States NSF grant DMS-0501039 for the support of his research.     

A Note on Tortrat Groups

A locally compact group G is called a Tortrat group if for any probability measure on G which is not idempotent, the closure of {gg ^–1 | gG} does not contain any idempotent measure. We show that a connected Lie group G is a Tortrat group if and only if for all gG all eigenvalues of Ad g are of absolute value 1. Together with well-known results this also implies that a connected locally compact group is a Tortrat group if and only if it is of polynomial growth.     

A Categorical Structure for the Virtual Braid Group

This article gives a new interpretation of the virtual braid group in terms of a strict monoidal category SC that is freely generated by one object and three morphisms, two of the morphisms corresponding to basic pure virtual braids and one morphism corresponding to a transposition in the symmetric group. This point of view makes many relationships between the virtual braid group and the pure virtual braid group apparent, and makes representations of the virtual braid groups and pure virtual braid groups via solutions to the algebraic Yang–Baxter Equation equally transparent. In this categorical framework, the virtual braid group has nothing to do with the plane and nothing to do with virtual crossings. It is a natural group associated with the structure of algebraic braiding.