Equalizers and coactions of groups

Martin Arkowitz; Mauricio Gutierrez

Fundamenta Mathematicae, Tome 173 (2002), p. 155-165 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $_{f} \subseteq G * H$ be the equalizer of fp and q:G*H → H. Then p restricts to an epimorphism $p_{f} {= p |}_{f} :_{f} \to G$ . A right inverse (section) $G \to_{f}$ 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.

Publié le : 2002-01-01

Zbl 1049.20011

EUDML-ID : urn:eudml:doc:282639

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     title = {Equalizers and coactions of groups},
     journal = {Fundamenta Mathematicae},
     volume = {173},
     year = {2002},
     pages = {155-165},
     zbl = {1049.20011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm171-2-3}
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Martin Arkowitz; Mauricio Gutierrez. Equalizers and coactions of groups. Fundamenta Mathematicae, Tome 173 (2002) pp. 155-165. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm171-2-3/