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Dynamical Properties of Additive Cellular Automata over finite abelian groups

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Journal of Donghua University(English Edition) 2023年第1期40卷 116-121页

作者：邓爱平王枫杰伍陈晨 College of Science Donghua UniversityShanghai 201620China

Some dynamical properties were discussed for additive cellular automata(CA)over finite abelian *** properties include surjection,ergodicity,sensitivity to initial conditions and positive *** 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 *** positive expansivity was proved to be preserved under the shift mappings for the general *** 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.

关键词： additive cellular automaton finite abelian group ergodicity sensitivity to initial condition positive expansivity

On the Average Number of Unitary Factors of finite abelian groups (Ⅱ)

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Acta Mathematica Sinica,English Series 2000年第4期16卷 549-554页

作者： Wenguang Zhai Department of Mathematics, Shandong Normal University. Jinan 250014. P. B. China Department of Mathematics Shandong Normal University Jinan 250014 P. R. China

Let t（G） be the number of unitary factors of finite abelian group G. In this paper we prove T（x）=∑(G≤（）t（G） =main terms+O(x(（1+2k）/（3+4k）for any exponent pair （k, 1/2+2K）. which improves on the exponen... 详细信息

关键词： Unitary factor finite abelian group Exponential sum Divisor problem

Weak Isomorphism of finite group

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Journal of Southwest Jiaotong University(English Edition) 2007年第1期15卷 80-83页

作者：蒲伟何军华 Departmentof Application Mathematics Southwest Jiaotong University Chengdu 610031 ChinaDepartment of Mathematics University of Electronic Science and Technology of ChinaChengdu 610054 China

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）.

关键词： Weak isomorphism finite abelian group Nilpotent gtoup p-Cvtoup