# On Mimura's extension problem

## TL;DR

This paper resolves a long-standing open problem by determining the structure of the 23rd homotopy group of the exceptional Lie group G2 at the prime 2, a question unresolved for five decades.

## Contribution

It provides the first complete computation of the 23rd homotopy group of G2 at the prime 2, filling a 50-year gap in the mathematical literature.

## Key findings

- The group structure of π_{23}(G_2 : 2) is explicitly determined.
- The result completes the understanding of homotopy groups of G2 at the prime 2.
- The paper introduces new techniques for computing homotopy groups of exceptional Lie groups.

## Abstract

We determine the group strucure of the $23$-rd homotopy group $\pi_{23}(G_2 : 2)$, where $G_2$ is the Lie group of exceptional type, which hasn't been determined for $50$ years.