p-elementary group
= p-elementary group
{title2=$E=P\times C,\quad P\text{ a }p\text{-group},\quad C\text{ cyclic},\ p\nmid|C|$}
A p-elementary group is a <direct product of groups> of a <p-group> and a cyclic group whose order is coprime to $p$. Either factor may be trivial. The coprime cyclic factor is central, a stronger requirement than merely having a cyclic subgroup with p-group quotient.