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Equalizers and coactions of groups

Martin ArkowitzMauricio Gutierrez — 2002

Fundamenta Mathematicae

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...

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