Verbal subgroup of group of prime power order

This article describes a property that arises as the conjunction of a subgroup property: verbal subgroup with a group property imposed on the ambient group: group of prime power order
View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

Definition

A verbal subgroup of group of prime power order is a subgroup of a group where the whole group is a group of prime power order (i.e., a finite $p$-group for some prime number $p$) and the subgroup is a verbal subgroup.

Examples

VIEW: subgroups satisfying this property | subgroups dissatisfying property verbal subgroup | subgroups whose group part dissatisfies property group of prime power order
VIEW: Related subgroup property satisfactions | Related subgroup property dissatisfactions

• The commutator subgroup and all members of the derived series and lower central series are verbal subgroups.
• The agemo subgroups are all verbal subgroups.
• Subgroups obtained via a combination of applying agemo and taking commutators are also verbal.

Relation with other properties

Weaker properties

• Fully invariant subgroup of group of prime power order
• Characteristic subgroup of group of prime power order
• Normal subgroup of group of prime power order