Subgroup with abelianization of maximum order

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Definition

Let P be a group of prime power order. A subgroup B of P is termed a subgroup with abelianization of maximum order if the order of the abelianization of B (i.e., the quotient of B by its commutator subgroup) is greater than or equal to the order of the abelianization of any subgroup of P.

Relation with other properties

Stronger properties