Thompson subgroup

In mathematical finite group theory, the Thompson subgroup formula_1 of a finite "p"-group "P" refers to one of several characteristic subgroups of "P". originally defined formula_1 to be the subgroup generated by the abelian subgroups of "P" of maximal rank. More often the Thompson subgroup formula_1 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 formula_1.