Group property-conditionally normal-potentially characteristic subgroup

From Groupprops
Jump to: navigation, search
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This term is related to: potentially characteristic subgroups characterization problem
View other terms related to potentially characteristic subgroups characterization problem | View facts related to potentially characteristic subgroups characterization problem

Definition

Let H be a subgroup of a group G, and \alpha be a group property. We say that H is normal-potentially characteristic in G relative to \alpha if there exists a group K containing G and satisfying \alpha such that G is a normal subgroup of K and H is a characteristic subgroup of K.

If we simply use the term normal-potentially characteristic subgroup, it means that \alpha is taken to be the tautology -- the property satisfied by all groups.

Relation with other properties

Stronger properties

Weaker properties