Group of prime power order whose derived subgroup is in the first agemo subgroup of its center
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
A group of prime power order whose derived subgroup is in the first agemo subgroup of its center is a group of prime power order , i.e., a finite -group for some prime number , such that the derived subgroup is contained in the first agemo subgroup of the center. In symbols:
In other words, every commutator is the power of some central element of the group.