# section of a group

A *section ^{}* of a group $G$ is
a quotient

^{}(http://planetmath.org/QuotientGroup) of a subgroup

^{}of $G$. That is, a section of $G$ is a group of the form $H/N$, where $H$ is a subgroup of $G$, and $N$ is a normal subgroup

^{}of $H$.

A group $G$ is said to be *involved in* a group $K$
if $G$ is isomorphic^{} to a section of $K$.

The relation^{} ‘is involved in’ is transitive^{} (http://planetmath.org/Transitive3),
that is, if $G$ is involved in $K$ and $K$ is involved in $L$,
then $G$ is involved in $L$.

Intuitively, ‘$G$ is involved in $K$’
means that all of the structure^{} of $G$ can be found inside $K$.

Title | section of a group |
---|---|

Canonical name | SectionOfAGroup |

Date of creation | 2013-03-22 17:15:04 |

Last modified on | 2013-03-22 17:15:04 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 11 |

Author | yark (2760) |

Entry type | Definition |

Classification | msc 20F99 |

Synonym | section |

Synonym | quotient of a subgroup |

Defines | involved in |