Group extension
id:
group-extension-216-3518976
title:
Group extension
text:
In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q and N are two groups, then G is an extension of Q by N if there is a short exact sequence
- 1 → N → ι G → π Q → 1. If G is an extension of Q by N, then G is a group, ι is a normal subgroup of G and the quotient group G / ι is isomorphic to the group Q. Group extensions arise in the context of the extension problem, where the groups Q and N are known and t
brand slug:
wiki
category slug:
encyclopedia
description:
Group for which a given group is a normal subgroup
original url:
https://en.wikipedia.org/wiki/Group_extension
date created:
2003-10-20T22:16:37Z
date modified:
2024-09-12T22:10:46Z
main entity:
{"identifier":"Q3041173","url":"https://www.wikidata.org/entity/Q3041173"}
image:
fields total:
13
integrity:
15