伽罗瓦定理真的错了吗?  

Is Galois's Theorem Really Wrong?

作　　者：杨保强 YANG Baoqiang(School of Mathematics and Computer Science,Yan'an University,Yan'an 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,延安716000

出　　处：《中国科技史杂志》2024年第1期67-76,共10页The Chinese Journal for the History of Science and Technology

基　　金：延安大学博士科研启动项目“本原方程的历史研究”(项目编号:YDBK2022-64);国家自然科学基金地区科学基金项目“非欧几何学的若干历史问题研究”(项目编号:12161086)。

摘　　要：1830年,伽罗瓦提出有关本原方程的一个定理。在数学史上,很多学者认为该定理对于本原群的刻画是错误的,但有一些研究者猜想伽罗瓦的定理可能无误,也许伽罗瓦的本原群隐含地假设了二重传递性。本文通过引入与之相应的“二重传递方程”的概念,利用古证复原或数学实操的方法复原伽罗瓦对于本原方程的真实认识,证实伽罗瓦定理中的“本原方程”实际所指乃二重传递方程,对应于二重传递群的结果,伽罗瓦的定理并无差错。In 1830,Galois put forward a theorem on primitive equations.Many scholars believed that this theorem was wrong for the characterization of primitive groups in the history of mathematics.Some researchers supposed that Galois's theorem should be correct,and that Galois was probably assuming implicitly double-transitivity.By introducing the corresponding concept of the"doubly transitive equation",this paper is to restore Galois's real thoughts by the method of mathematical practice or paradigm of recovery,and to prove that"primitive equation"in Galois's theorem actually refers to the doubly transitive equation.According to the corresponding result of the doubly transitive group,nothing is wrong in this theorem.

关 键 词：伽罗瓦 本原方程 二重传递群 数学实操 古证复原 

分 类 号：N09[自然科学总论—科学技术哲学] O151.1[理学—数学]