Equalizers and coactions of groups

Martin Arkowitz, and Mauricio Gutierrez. "Equalizers and coactions of groups." Fundamenta Mathematicae 171.2 (2002): 155-165. <http://eudml.org/doc/282639>.

@article{MartinArkowitz2002,
abstract = {If f:G → H is a group homomorphism and p,q are the projections from the free product G*H onto its factors G and H respectively, let the group $_\{f\}⊆ G*H$ be the equalizer of fp and q:G*H → H. Then p restricts to an epimorphism $p_\{f\} = p|_\{f\}:_\{f\} → G$. A right inverse (section) $G → _\{f\}$ of $p_\{f\}$ is called a coaction on G. In this paper we study $_\{f\}$ and the sections of $p_\{f\}$. We consider the following topics: the structure of $_\{f\}$ as a free product, the restrictions on G resulting from the existence of a coaction, maps of coactions and the resulting category of groups with a coaction and associativity of coactions.},
author = {Martin Arkowitz, Mauricio Gutierrez},
journal = {Fundamenta Mathematicae},
keywords = {free products; equalizers; coactions; homomorphisms; projections},
language = {eng},
number = {2},
pages = {155-165},
title = {Equalizers and coactions of groups},
url = {http://eudml.org/doc/282639},
volume = {171},
year = {2002},
}

TY - JOUR
AU - Martin Arkowitz
AU - Mauricio Gutierrez
TI - Equalizers and coactions of groups
JO - Fundamenta Mathematicae
PY - 2002
VL - 171
IS - 2
SP - 155
EP - 165
AB - If f:G → H is a group homomorphism and p,q are the projections from the free product G*H onto its factors G and H respectively, let the group $_{f}⊆ G*H$ be the equalizer of fp and q:G*H → H. Then p restricts to an epimorphism $p_{f} = p|_{f}:_{f} → G$. A right inverse (section) $G → _{f}$ of $p_{f}$ is called a coaction on G. In this paper we study $_{f}$ and the sections of $p_{f}$. We consider the following topics: the structure of $_{f}$ as a free product, the restrictions on G resulting from the existence of a coaction, maps of coactions and the resulting category of groups with a coaction and associativity of coactions.
LA - eng
KW - free products; equalizers; coactions; homomorphisms; projections
UR - http://eudml.org/doc/282639
ER -