Let $p$ be a D571: Prime integer.

Then $G$ is a

**P-group**with respect to $p$ if and only if \begin{equation} \forall \, g \in G : \exists \, n \in \mathbb{N} : |g| = p^n \end{equation}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Enclosed binary operation

▾ Groupoid

▾ Semigroup

▾ Monoid

▾ Group

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Enclosed binary operation

▾ Groupoid

▾ Semigroup

▾ Monoid

▾ Group

Formulation 0

Let $G$ be a D22: Group.

Let $p$ be a D571: Prime integer.

Then $G$ is a**P-group** with respect to $p$ if and only if
\begin{equation}
\forall \, g \in G : \exists \, n \in \mathbb{N} : |g| = p^n
\end{equation}

Let $p$ be a D571: Prime integer.

Then $G$ is a

Child definitions