---
tag: 6MF2ZQJ7KQ
kind: concept
name: Thompson subgroup
sources:
  - wikipedia: en:5662011@r1246736639
    locator: Thompson subgroup
    note: adopted
    mention: wikipedia://en/5662011
    sections: [Summary]
same_as:
  wikidata: Q7795824
  wikipedia: Thompson subgroup
inventory: [JQP9T4XKJ2]
---

## Summary

"Thompson subgroup" can also mean an analogue of the Weyl group used in the classical involution theorem In finite group theory, a branch of mathematics, the **Thompson subgroup** $J(P)$ of a finite [[*p*-group|06QYRTX9KQ]] *P* refers to one of several [[characteristic subgroups|01CS8Q2APC]] of *P*. (txt) originally defined $J(P)$ to be the subgroup generated by the [[abelian|071DDFVG4J]] [[subgroups|0X1JXT47GA]] of *P* of maximal rank. More often the Thompson subgroup $J(P)$ is defined to be the subgroup generated by the abelian subgroups of *P* of maximal [[order|0B85S2V2DR]] or the subgroup generated by the elementary abelian subgroups of *P* of maximal rank. In general these three subgroups can be different, though they are all called the Thompson subgroup and denoted by $J(P)$.