JournalsrsmupVol. 144pp. 197–215

Quasibases for nonseparable pp-groups

  • Otto Mutzbauer

    Universität Würzburg, Germany
  • Elias Toubassi

    University of Arizona, Tucson, USA
  • Andrija Vodopivec

    Besigheim, Germany
Quasibases for nonseparable $p$-groups cover
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Abstract

This paper is an extension of the work developed in [4] on quasibases of abelian pp-groups and based on the doctoral dissertation ofAndrija Vodopivec [5].We introduce the ideas of a δ\delta-combination and height of an inductive quasibasis and show that the height of a quasibasis is invariant for related inductive quasibases. Moreover, an abelian pp-group is separable if and only if the heights of all δ\delta-combinations are zero. Finally, we show that an abelian pp-group is not reduced if and only if there exists a δ\delta-combination with infinite height.

Cite this article

Otto Mutzbauer, Elias Toubassi, Andrija Vodopivec, Quasibases for nonseparable pp-groups. Rend. Sem. Mat. Univ. Padova 144 (2020), pp. 197–215

DOI 10.4171/RSMUP/65