P-hyperelementary group

Definition
A finite group is termed $$p$$-hyperelementary if it satisfies the following equivalent conditions:


 * 1) It is the internal semidirect product of a cyclic group of order relatively prime to $$p$$ with a $$p$$-group.
 * 2) It is the internal semidirect product of a cyclic group and a $$p$$-group.
 * 3) It contains a cyclic normal $$p$$-complement.

Stronger properties

 * Weaker than::p-elementary group