Subgroup with abelianization of maximum order
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
This article is about a maximality notion among subgroups, related to abelianness or small class, in a group of prime power order.
View other such notions
Let be a group of prime power order. A subgroup of is termed a subgroup with abelianization of maximum order if the order of the abelianization of (i.e., the quotient of by its commutator subgroup) is greater than or equal to the order of the abelianization of any subgroup of .