Centralizer-large subgroup

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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]

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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 $P$ is a group of prime power order. A subgroup $A$ of $P$ is termed a centralizer-large subgroup if $|A||C_{P}(A)|\geq |B||C_{P}(B)|$ for all subgroups $P$ of $B$.

Relation with other properties

Stronger properties

• Centrally large subgroup

Weaker properties

• c-closed subgroup