Join of abelian subgroups of maximum rank

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Template:Prime-parametrized subgroup-defining function

Definition

Let P be a group of prime power order. The join of Abelian subgroups of maximum rank in P, sometimes denoted J(P) and also termed the Thompson subgroup, is defined as the subgroup of P generated by all abelian subgroups of maximum rank in P.

Note that the term Thompson subgroup is also used for the join of abelian subgroups of maximum order and for the join of elementary abelian subgroups of maximum order.