Cocentral subgroup of normalizer

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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 is a variation of cocentral subgroup|Find other variations of cocentral subgroup |

Definition

Symbol-free definition

A subgroup of a group is said to be a cocentral subgroup of normalizer if it is a cocentral subgroup of its normalizer.

Definition with symbols

A subgroup H of a group G is said to be a cocentral subgroup of normalizer if HZ(N_G(H)) = N_G(H) where Z(N_G(H)) denotes the center of N_G(H) and N_G(H) denotes the normalizer of H.

Formalisms

In terms of the in-normalizer operator

This property is obtained by applying the in-normalizer operator to the property: cocentral subgroup
View other properties obtained by applying the in-normalizer operator

Relation with other properties

Stronger properties

Weaker properties

Metaproperties

Trimness

This subgroup property is trim -- it is both trivially true (true for the trivial subgroup) and identity-true (true for a group as a subgroup of itself).
View other trim subgroup properties | View other trivially true subgroup properties | View other identity-true subgroup properties