In mathematical finite group theory, the Thompson subgroup J(P) of a finite p-group P refers to one of several normal subgroups. originally defined of J(P) to be the subgroup generated by the abelian subgroups of P of maximal order. More often the Thompson subgroup J(P) is defined to be the subgroup generated by the elementary abelian subgroups of P of maximal order. A third variation defines it to be the subgroup generated by the 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).