# ZJe-subgroup

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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

Let be a prime number and be a finite p-group. The **ZJe-subgroup** of , denoted , is defined as the center of the join of elementary abelian subgroups of maximum order (denoted ). It is related to, but not necessarily the same as, the ZJ-subgroup, which is the center of the join of abelian subgroups of maximum order (denoted ).

and are two of the Thompson subgroups.