Thompson subgroup

This article is about a definition in group theory that is standard among the group theory community (or sub-community that dabbles in such things) but is not very basic or common for people outside.
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Definition

Definition with symbols

Let $P$ be a group and $p$ a prime. The Thompson subgroup of $P$ corresponding to $p$, denoted as $J(P)$, is defined as the subgroup generated by all the elementary Abelian $p$-subgroups of maximum order.

The notion is typically studied for a group of prime characteristic type viz a group of characteristic $p$-type.