JournalsrsmupVol. 144pp. 253–270

Density of indecomposable locally finite groups

  • Saharon Shelah

    The Hebrew University of Jerusalem, Israel and The State University of New Jersey, Piscataway, USA
Density of indecomposable locally finite groups cover
Download PDF

A subscription is required to access this article.

Abstract

We prove that for any locally finite group there is an extension of the same cardinality which is indecomposable for almost all regular cardinals smaller than its cardinality. Note that a group GG is called θ\theta-indecomposable when for every increasing sequence Gi ⁣:i<θ\langle G_i\colon i < \theta \rangle of subgroups with union GG there is i<θi < \theta such that G=GiG= G_i.

Cite this article

Saharon Shelah, Density of indecomposable locally finite groups. Rend. Sem. Mat. Univ. Padova 144 (2020), pp. 253–270

DOI 10.4171/RSMUP/68