# Centralizer-large subgroup

From Groupprops

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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.

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## Statement

Suppose is a group of prime power order. A subgroup of is termed a **centralizer-large subgroup** if for all subgroups of .