Let $p$ be a D571: Prime integer.

A D22: Group $H$ is a

**P-subgroup**of $G$ with respect to $p$ if and only if

(1) | $H$ is a D496: Subgroup of $G$ |

(2) | $H$ is a D1568: P-group with respect to $p$ |

▾ 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

▾ P-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

▾ P-group

Formulation 0

Let $G$ be a D22: Group.

Let $p$ be a D571: Prime integer.

A D22: Group $H$ is a**P-subgroup** of $G$ with respect to $p$ if and only if

Let $p$ be a D571: Prime integer.

A D22: Group $H$ is a

(1) | $H$ is a D496: Subgroup of $G$ |

(2) | $H$ is a D1568: P-group with respect to $p$ |