This paper is an extension of the work developed in  on quasibases of abelian -groups and based on the doctoral dissertation ofAndrija Vodopivec .We introduce the ideas of a -combination and height of an inductive quasibasis and show that the height of a quasibasis is invariant for related inductive quasibases. Moreover, an abelian -group is separable if and only if the heights of all -combinations are zero. Finally, we show that an abelian -group is not reduced if and only if there exists a -combination with infinite height.
Cite this article
Otto Mutzbauer, Elias Toubassi, Andrija Vodopivec, Quasibases for nonseparable -groups. Rend. Sem. Mat. Univ. Padova 144 (2020), pp. 197–215DOI 10.4171/RSMUP/65