标题： 关于矩形托达括号和小田的扩展问题 显示英文标题

标题： On rectangular Toda brackets and Oda's extension problems

摘要： 本文研究了在2局部化下同伦群$\pi_{39}(S^{6})$,$\pi_{40}(S^{7})$和$\pi_{41}(S^{8})$的\textit{奥达N.}扩展问题，这些问题在过去四十多年里一直未能解决。我们引入了一种用于不稳定同伦群确定理论的工具，即矩形托达括号，通过这种方法，我们能够解决这三个同伦群的扩展问题。 显示英文摘要

摘要： This paper tackles \textit{N. Oda}'s extension problems for the homotopy groups $\pi_{39}(S^{6})$, $\pi_{40}(S^{7})$, and $\pi_{41}(S^{8})$ localized at 2, the issues having eluded resolution for more than four decades. We introduce a tool for the theory of determinations of unstable homotopy groups, namely, the rectangular Toda bracket, by which we are able to solve the extension problems with respect to these three homotopy groups.