Equalizers and coactions of groups

Tom 171 / 2002

Martin Arkowitz, Mauricio Gutierrez Fundamenta Mathematicae 171 (2002), 155-165 MSC: Primary 20E06; Secondary 20F99. DOI: 10.4064/fm171-2-3


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.


  • Martin ArkowitzMathematics Department
    Dartmouth College
    Hanover, NH 03755, U.S.A.
  • Mauricio GutierrezMathematics Department
    Tufts University
    Medford, MA 02155, U.S.A.

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