Density of indecomposable locally finite groups

Saharon Shelah

doi:10.4171/RSMUP/68

Density of indecomposable locally finite groups

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 θ-indecomposable when for every increasing sequence hG_i W i < θi of subgroups with union G there is i < θ such that G D G_i.

Original language	English
Pages (from-to)	253-270
Number of pages	18
Journal	Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova
Volume	144
DOIs	https://doi.org/10.4171/RSMUP/68
State	Published - 2020

Bibliographical note

Publisher Copyright:
© 2020, European Mathematical Society Publishing House. All rights reserved.

Keywords

Applications of model theory
Canonical extension
Groups
Indecomposable group
Locally finite groups
Model theory

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10.4171/RSMUP/68

Cite this

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AB - 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 θ-indecomposable when for every increasing sequence hGi W i < θi of subgroups with union G there is i < θ such that G D Gi.

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Density of indecomposable locally finite groups

Abstract

Bibliographical note

Keywords

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