Equalizers and coactions of groups

Martin Arkowitz¹ ; Mauricio Gutierrez²

¹ Mathematics Department Dartmouth College Hanover, NH 03755, U.S.A.
² Mathematics Department Tufts University Medford, MA 02155, U.S.A.

Fundamenta Mathematicae, Tome 171 (2002) no. 2, pp. 155-165.

Résumé

If $f:G\to H$ 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 ${\cal E}_f\subseteq G*H$ be the equalizer of $fp$ and $q:G*H\to H$. Then $p$ restricts to an epimorphism $p_f=p|{\cal E}_f:{\cal E}_f\to G$. A right inverse (section) $G\to {\cal E}_f$ of $p_f$ is called a coaction on $G$. In this paper we study ${\cal E}_f$ and the sections of $p_f$. We consider the following topics: the structure of ${\cal E}_f$ 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.

Détail

DOI : 10.4064/fm171-2-3

Keywords: group homomorphism projections product g*h its factors respectively group cal subseteq g*h equalizer g*h restricts epimorphism cal cal right inverse section cal called coaction paper study cal sections consider following topics structure cal product restrictions resulting existence coaction maps coactions resulting category groups coaction associativity coactions