Sub-isomorph-free subgroup

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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-free 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-free subgroup of $H_{i+1}$.

Effect of property operators

In terms of the subordination operator

This property is obtained by applying the subordination operator to the property: isomorph-free subgroup
View other properties obtained by applying the subordination operator

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