Algorithmic theory of solvable groups

IF 0.2 Q4 MATHEMATICS, APPLIED

Prikladnaya Diskretnaya Matematika Pub Date : 2021-01-01 DOI:10.17223/20710410/52/2

V. Roman’kov

引用次数: 1

Abstract

The purpose of this survey is to give some picture of what is known about algorithmic and decision problems in the theory of solvable groups. We will provide a number of references to various results, which are presented without proof. Naturally, the choice of the material reported on reflects the author’s interests and many worthy contributions to the field will unfortunately go without mentioning. In addition to achievements in solving classical algorithmic problems, the survey presents results on other issues. Attention is paid to various aspects of modern theory related to the complexity of algorithms, their practical implementation, random choice, asymptotic properties. Results are given on various issues related to mathematical logic and model theory. In particular, a special section of the survey is devoted to elementary and universal theories of solvable groups. Special attention is paid to algorithmic questions regarding rational subsets of groups. Results on algorithmic problems related to homomorphisms, automorphisms, and endomorphisms of groups are presented in sufficient detail.

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可解群的算法理论

这个调查的目的是给什么是已知的算法和决策问题在可解群理论的一些图片。我们将提供一些对各种结果的参考，这些结果是没有证据的。自然，报告材料的选择反映了作者的兴趣，不幸的是，对该领域的许多有价值的贡献将被忽略。除了在解决经典算法问题方面取得的成就外，调查还展示了在其他问题上的成果。关注与算法复杂性有关的现代理论的各个方面，它们的实际实现，随机选择，渐近性质。给出了与数理逻辑和模型论有关的各种问题的结果。特别地，调查的一个特殊部分致力于基本和普遍理论的可解群。特别关注关于群的合理子集的算法问题。关于群的同态、自同态和自同态的算法问题，给出了足够详细的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Prikladnaya Diskretnaya Matematika MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

50.00%

发文量

期刊介绍： The scientific journal Prikladnaya Diskretnaya Matematika has been issued since 2008. It was registered by Federal Control Service in the Sphere of Communications and Mass Media (Registration Witness PI № FS 77-33762 in October 16th, in 2008). Prikladnaya Diskretnaya Matematika has been selected for coverage in Clarivate Analytics products and services. It is indexed and abstracted in SCOPUS and WoS Core Collection (Emerging Sources Citation Index). The journal is a quarterly. All the papers to be published in it are obligatorily verified by one or two specialists. The publication in the journal is free of charge and may be in Russian or in English. The topics of the journal are the following: 1.theoretical foundations of applied discrete mathematics – algebraic structures, discrete functions, combinatorial analysis, number theory, mathematical logic, information theory, systems of equations over finite fields and rings; 2.mathematical methods in cryptography – synthesis of cryptosystems, methods for cryptanalysis, pseudorandom generators, appreciation of cryptosystem security, cryptographic protocols, mathematical methods in quantum cryptography; 3.mathematical methods in steganography – synthesis of steganosystems, methods for steganoanalysis, appreciation of steganosystem security; 4.mathematical foundations of computer security – mathematical models for computer system security, mathematical methods for the analysis of the computer system security, mathematical methods for the synthesis of protected computer systems;[...]