Sub-(isomorph-normal 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

A subgroup H of a group G is termed a sub-(isomorph-normal characteristic) subgroup if there exists an ascending chain of subgroups:

H = H_0 \le H_1 \le H_2 \le \dots \le H_n = G

such that each H_i is an isomorph-normal characteristic subgroup of H_{i+1}, i.e., H_i is characteristic in H_{i+1}, and H_i is isomorph-normal in H_{i+1}: every subgroup of H_{i+1} isomorphic to H_i is normal.

Relation with other properties

Stronger properties

Weaker properties

Metaproperties

Transitivity

This subgroup property is transitive: a subgroup with this property in a subgroup with this property, also has this property in the whole group.
ABOUT THIS PROPERTY: View variations of this property that are transitive | View variations of this property that are not transitive
ABOUT TRANSITIVITY: View a complete list of transitive subgroup properties|View a complete list of facts related to transitivity of subgroup properties |Read a survey article on proving transitivity