Maximal among abelian characteristic subgroups

From Groupprops
Jump to: navigation, search
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]

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]


Symbol-free definition

A subgroup of a group is termed maximal among Abelian characteristic subgroups if it is an Abelian characteristic subgroup, and is not properly contained in any Abelian characteristic subgroup.


In terms of the maximal operator

This property is obtained by applying the maximal operator to the property: Abelian characteristic subgroup
View other properties obtained by applying the maximal operator

Relation with other properties

Weaker properties


Facts about such subgroups in nilpotent groups and p-groups

Here are some facts about the possibility of existence of multiple subgroups that are maximal among Abelian characteristic subgroups: