Thompson subgroup

In finite group theory, a branch of mathematics, the Thompson subgroup

of a finite p-group P refers to one of several characteristic subgroups of P. John G. Thompson (1964) originally defined

to be the subgroup generated by the abelian subgroups of P of maximal rank.

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