Thompson subgroup

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. 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 $$J(P)$$.