Abelian subgroup of maximum order which is normal

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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: abelian subgroup of maximum order and abelian normal subgroup of group of prime power order
View other subgroup property conjunctions | view all subgroup properties
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: abelian subgroup of maximum order and abelian normal subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

Suppose G is a group of prime power order, i.e., G is a finite p-group for some prime number p. Suppose H is a subgroup of G. We say that H is an abelian subgroup of maximum order which is normal if H is an abelian subgroup of maximum order in G and H is also a normal subgroup of G.

Relation with other properties

Weaker properties