Retract (group theory)
id:
retract-group-theory-300-16106783
title:
Retract (group theory)
text:
In mathematics, in the field of group theory, a subgroup of a group is termed a retract if there is an endomorphism of the group that maps surjectively to the subgroup and is the identity on the subgroup. In symbols, H is a retract of G if and only if there is an endomorphism σ : G → G such that σ = h for all h ∈ H and σ ∈ H for all g ∈ G . The endomorphism σ is an idempotent element in the transformation monoid of endomorphisms, so it is called an idempotent endomorphism or a retraction. The fo
brand slug:
wiki
category slug:
encyclopedia
description:
Subgroup of a group in mathematics
original url:
https://en.wikipedia.org/wiki/Retract_(group_theory)
date created:
date modified:
2023-12-03T06:03:10Z
main entity:
{"identifier":"Q7316893","url":"https://www.wikidata.org/entity/Q7316893"}
image:
fields total:
13
integrity:
14