Subgroup of abelian normal subgroup

Symbol-free definition
A subgroup of a group is termed a subgroup of Abelian normal subgroup if it satisfies the following equivalent conditions:


 * 1) It is a subgroup of an Abelian normal subgroup.
 * 2) It is a normal subgroup of an Abelian normal subgroup.
 * 3) It is a central subgroup (i.e., it is contained in the center) of a normal subgroup.

Stronger properties

 * Weaker than::Central subgroup
 * Weaker than::Abelian normal subgroup
 * Weaker than::2-subnormal subgroup of least prime order:

Weaker properties

 * Stronger than::Central factor of normal subgroup
 * Stronger than::Abelian 2-subnormal subgroup
 * Stronger than::2-subnormal subgroup
 * Stronger than::Right-transitively 2-subnormal subgroup