Sub-isomorph-free 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

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

Relation with other properties

Stronger properties

• Isomorph-free subgroup

Weaker properties

• Sub-(isomorph-normal characteristic) subgroup
• Left-transitively WNSCDIN-subgroup
• Characteristic subgroup
• Normal subgroup

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.
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