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
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Suppose is a prime number and is a finite p-group. The join of elementary abelian subgroups of maximum order in , denoted , is defined as the join of all the elementary abelian subgroups that have maximum order among elementary abelian subgroups of .
This is one of the three Thompson subgroups. In some contexts, it is referred to as the Thompson subgroup.