Join of elementary abelian subgroups of maximum order

This article defines a subgroup-defining function, viz., a rule that takes a group and outputs a unique subgroup
View a complete list of subgroup-defining functions OR View a complete list of quotient-defining functions

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.