Characteristic sub-APS

From Apstheory

This article defines terminology that is local to the wiki. For its use outside the wiki, please give full definitions

This article describes a property that can be evaluated for a sub-APS of an APS of groups

Contents 1 Definition 2 Relation with other properties 2.1 Stronger properties 2.2 Weaker properties

Definition

A sub-APS of an APS of groups is termed characteristic if for every member of the APS, the corresponding member of the sub-APS is characteristic in it. That is, a sub-APS Failed to parse (Can't write to or create math temp directory): H

of an APS Failed to parse (Can't write to or create math temp directory): G
is termed characteristic if for every Failed to parse (Can't write to or create math temp directory): n

, Failed to parse (Can't write to or create math temp directory): H_n

is a [[[:Template:Groupprops]] characteristic subgroup] of Failed to parse (Can't write to or create math temp directory): G_n

.

Relation with other properties

Stronger properties

• [[Fully characteristic

Weaker properties

• Normal sub-APS
• Weakly characteristic sub-APS