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
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.
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
@article{10_4153_CMB_2011_172_3,
author = {Oancea, D.},
title = {Coessential {Abelianization} {Morphisms} in the {Category} of {Groups}},
journal = {Canadian mathematical bulletin},
pages = {395--399},
year = {2013},
volume = {56},
number = {2},
doi = {10.4153/CMB-2011-172-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-172-3/}
}
Cité par Sources :