Geodesic
Coessential Abelianization Morphisms in the Category of Groups
Canadian mathematical bulletin, Tome 56 (2013) no. 2, pp. 395-399

Voir la notice de l'article provenant de la source Cambridge University Press

An epimorphism $\phi :\,G\,\to \,H$ of groups, where $G$ has rank $n$ , is called coessential if every (ordered) generating $n$ -tuple of $H$ can be lifted along $\phi $ to a generating $n$ -tuple for $G$ . We discuss this property in the context of the category of groups, and establish a criterion for such a group $G$ to have the property that its abelianization epimorphism $G\,\to \,{G}/{[G,G]}\;$ , where $[G,\,G]$ is the commutator subgroup, is coessential. We give an example of a family of 2-generator groups whose abelianization epimorphism is not coessential. This family also provides counterexamples to the generalized Andrews–Curtis conjecture.
DOI : 10.4153/CMB-2011-172-3
Mots-clés : 20F05, 20F99, 20J15, coessential epimorphism, Nielsen transformations, Andrew-Curtis transformations 
Oancea, D. Coessential Abelianization Morphisms in the Category of Groups. Canadian mathematical bulletin, Tome 56 (2013) no. 2, pp. 395-399. doi: 10.4153/CMB-2011-172-3
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