Join of elementary abelian subgroups of maximum order

Definition
Suppose $$p$$ is a prime number and $$P$$ is a finite p-group. The join of elementary abelian subgroups of maximum order in $$P$$, denoted $$J_e(P)$$, is defined as the join of all the elementary abelian subgroups that have maximum order among elementary abelian subgroups of $$P$$.

This is one of the three Thompson subgroups. In some contexts, it is referred to as the Thompson subgroup.