Group having an abelian normal non-central subgroup

From Groupprops
Jump to: navigation, search
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

Definition

A group having an Abelian normal non-central subgroup is a group satisfying the following equivalent conditions:

  1. There exists an Abelian normal subgroup not contained inside the center
  2. There exists an Abelian normal subgroup properly containing the center

Relation with other properties

Stronger properties