Weakly image-closed characteristic 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]

Definition

Definition with symbols

A subgroup H of a group G is termed a weakly image-closed characteristic subgroup of G if, for any normal subgroup N of G contained in H, the quotient group H/N is a characteristic subgroup of the quotient group G/N.

Formalisms

In terms of the weak image condition operator

This property is obtained by applying the weak image condition operator to the property: characteristic subgroup
View other properties obtained by applying the weak image condition operator

Relation with other properties

Stronger properties

Weaker properties