A. Fomin and W. Wickless Quotient divisible abelian groups
Proceedings of the Amer.Math.Soc., vol. 126, no. 1, 1998, 45-52.
Annotation
An abelian group G is called quotient divisible if G is of finite
torsion-free rank and there exists a free subgroup F G such that G=F is
divisible. The class of quotient divisible groups contains the torsion-free nite
rank quotient divisible groups introduced by Beaumont and Pierce and essen-
tially contains the class G of self-small mixed groups which has recently been
investigated by several authors. We construct a duality from the category of
quotient divisible groups and quasi-homomorphisms to the category of torsion-
free nite rank groups and quasi-homomorphisms. Our duality when restricted
to torsion-free quotient divisible groups coincides with the duality of Arnold
and when restricted to G coincides with the duality previously constructed by
the authors.
G such that G=F is
divisible. The class of quotient divisible groups contains the torsion-free nite
rank quotient divisible groups introduced by Beaumont and Pierce and essen-
tially contains the class G of self-small mixed groups which has recently been
investigated by several authors. We construct a duality from the category of
quotient divisible groups and quasi-homomorphisms to the category of torsion-
free nite rank groups and quasi-homomorphisms. Our duality when restricted
to torsion-free quotient divisible groups coincides with the duality of Arnold
and when restricted to G coincides with the duality previously constructed by
the authors.