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]
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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