Thompson subgroup

"Thompson subgroup" can also mean an analogue of the Weyl group used in the classical involution theorem

In mathematical finite group theory, the Thompson subgroup J(P) of a finite p-group P refers to one of several characteristic subgroups of P. 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