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

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