Characteristic direct factor of nilpotent group
This article describes a property that arises as the conjunction of a subgroup property: characteristic direct factor with a group property imposed on the ambient group: nilpotent group
View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup
- is a nilpotent group and is a characteristic direct factor of (i.e., is both a characteristic subgroup of and a direct factor of ).
- is a nilpotent group and is a fully invariant direct factor of (i.e., is both a fully invariant subgroup of and a direct factor of ). This has other equivalent formulations; see equivalence of definitions of fully invariant direct factor.
Equivalence of definitions
Further information: equivalence of definitions of characteristic direct factor of nilpotent group
The equivalence follows indirectly from the fact that nontrivial subgroup of nilpotent group has nontrivial homomorphism to center.