Join of elementary abelian subgroups of maximum order

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This article defines a subgroup-defining function, viz., a rule that takes a group and outputs a unique subgroup
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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.