Thompson subgroup

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title: "Thompson subgroup" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["finite-groups"] topic_path: "general/finite-groups" source: "https://en.wikipedia.org/wiki/Thompson_subgroup" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

In finite group theory, a branch of mathematics, the Thompson subgroup J(P) of a finite p-group P refers to one of several characteristic subgroups of P. originally defined J(P) to be the subgroup generated by the abelian subgroups 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 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).

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