Thompson subgroup

"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 P refers to one of several characteristic subgroups of P. John G. Thompson (1964) 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 $J(P)$.

See also

• Glauberman normal p-complement theorem
• ZJ theorem
• Puig subgroup, a subgroup analogous to the Thompson subgroup