Quasi-locally finite polynomial endomorphisms

If F is a polynomial endomorphism of , let denote the field of rational functions such that . We will say that F is quasi-locally finite if there exists a nonzero such that p(F) = 0. This terminology comes out from the fact that this definition is less restrictive than the one of locally finite endomorphisms made in Furter, Maubach (J Pure Appl Algebra 211(2):445–458, 2007). Indeed, F is called locally finite if there exists a nonzero such that p(F) = 0. In the present paper, we show that F is quasi-locally finite if and only if for each the sequence is a linear recurrent sequence. Therefore, this notion is in some sense natural. We also give a few basic results on such endomorphisms. For example: they satisfy the Jacobian conjecture.     

有限ATI-群的类保持Coleman自同构

设G是一个有限群,对G的任意阿贝尔子群A及任意g∈G,若A∩A~g=1或A,则称G为一个ATI-群.本文证明了,对任意p∈τ(G),如果ATI-群G的一个p-方幂阶类保持自同构在G的任意Sylow子群上的限制等于G的某个内自同构的限制,则它必定是一个内自同构.作为该结果的一个直接推论,我们也证明了有限ATI-群G有正规化性质.     

On Holomorphic Automorphisms of a Class of Non-homogeneous Rigid Hypersurfaces in C^N＋1

The author determines the real-analytic infinitesimal CR automorphisms of a class of non-homogeneous rigid hypersurfaces in C^N＋1 near the origin, and the connected component containing the identity transformation of all locally holomorphic automorphisms of these hypersurfaces near the origin.     

Semicomplete Permutational Wreath Products

A group is called semicomplete if every automorphism which induces the identity on the factor commutator group is inner. In this paper, we study the connection of the semicompleteness of the permutational wreath product W of two groups with the semicompleteness of these groups. We give necessary conditions under which the group W is semicomplete.2000 Mathematics Subject Classification: 20E22, 20E36     

New classes of test polynomials of polynomial algebras

A polynomialp in a polynomial algebra over a field is called a test polynomial if any endomorphism of the polynomial algebra that fixesp is an automorphism. some classes of new test polynomials recognizing nonlinear automorphisms of polynomial algebras are given. In the odd prime characteristic case, test polynomials recognizing non-semisimple automorphisms are also constructed. Project supported by the National Natural Science Foundation of China (Grant No. 19631100) and University of Hong Kong RGC Fundable Grant 344/024/0004.     

Automorphism Groups of Trees Acting Locally with Affine Permutations

We consider the structure of groups that act on a p ⁿ -regular tree in a vertex transitive way with the local action (i.e. the action of the vertex stabilizer on the link) isomorphic to the group of affine transformations on a finite affine line.     

一类推广的Virasoro-like李代数

构造了一类无限维李代数,它是Virasoro-like李代数的推广.研究了这类李代数的两类自同构,这两类自同构均关于映射的合成构成自同构群,一类同构于对称群S3,另一类同构于Klein交换群.得到了这类李代数一些特殊的自同态、中心.证明了这类李代数不是半单李代数.     

The automorphism group of the rank 2 Lie algebra free in the variety \mathfrak{A}\mathfrak{N}_2

We study the location of some finite subgroups in the automorphism group of the rank 2 Lie algebra free in the variety $\mathfrak{A}\mathfrak{N}_2 $ .     

Cyclotomic Polynomials and Finite Automorphisms of Groups

We introduce minimal polynomials for finite automorphisms of commutative groups and relate them to the exponent of the fixed points and to the reducibility of the group. Some results can be extended to the noncommutative case.     

Automorphisms of Free Left Nilpotent Leibniz Algebras and Fixed Points

ABSTRACT

Let F _m (N) be the free left nilpotent (of class two) Leibniz algebra of finite rank m, with m ≥ 2. We show that F _m (N) has non-tame automorphisms and, for m ≥ 3, the automorphism group of F _m (N) is generated by the tame automorphisms and one more non-tame IA-automorphism. Let F(N) be the free left nilpotent Leibniz algebra of rank greater than 1 and let G be an arbitrary non-trivial finite subgroup of the automorphism group of F(N). We prove that the fixed point subalgebra F(N) ^G is not finitely generated.