英语翻译1831年伽罗瓦在研究代数方程的解的过程中首次提出了“群”这一术语,并把代数方程的问题转化为群论的问题来解决.群论把人类从偏重计算研究的思维方式转变为用结构观念研究的

Question

英语翻译
1831年伽罗瓦在研究代数方程的解的过程中首次提出了“群”这一术语,并把代数方程的问题转化为群论的问题来解决.群论把人类从偏重计算研究的思维方式转变为用结构观念研究的思维方式,这个理论迅速发展成为一门崭新的数学分支,对近世代数的形成和发展产生了巨大影响,而且其应用范围已经深入到科学技术的各个领域.有限群的结构问题一直是群论研究中的热点,理论上已经完全解决了有限可换群结构,而有限非可换群结构则较为复杂.本文利用不变因子定理计算确定出了200阶以内所有可换群的类型,并介绍了15阶以内非可换群的结构.

Answer 1

1831 Galois in the process of the solution of algebraic equations in the study,which was first a "group" of the term.and the conversion of group theory,algebraic equations to solve the problem.Study group on mankind emphasis way of thinking used to study the concept of the structure of the mode of thinking,This theory developed rapidly into a new branch of mathematics,on the formation and development of Modern Algebra had a tremendous impact,The scope and depth of the application of science and technology in various fields.The structure has been limited research is a hot group theory,theory has been completely resolved available for a limited group structure.and limited non-abelian group structure more complex.Theorem factor calculated using the same order of 200% for all types of groups.and the non-abelian group of 15 bands within the structure.