### Saharon Shelah

The Hebrew University of Jerusalem, Israel and The State University of New Jersey, Piscataway, USA

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## 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 $G$ is called $\theta$-*indecomposable* when for every increasing sequence $\langle G_i\colon i < \theta \rangle$ of subgroups with union $G$ there is $i < \theta$ such that $G= G_i$.

## 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