On universal locally finite groups

Rami Grossberg*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

We deal with the question of existence of a universal object in the category of universal locally finite groups; the answer is negative for many uncountable cardinalities; for example, for 2א0, and assuming G.C.H. for every cardinal whose confinality is >א0. However, if λ>κ when κ is strongly compact and of λ=א0, then there exists a universal locally finite group of cardinality λ. The idea is to use the failure of the amalgamation property in a strong sense. We shall also prove the failure of the amalgamation property for universal locally finite groups by transferring the kind of failure of the amalgamation property from LF into ULF.

Original languageEnglish
Pages (from-to)289-302
Number of pages14
JournalIsrael Journal of Mathematics
Volume44
Issue number4
DOIs
StatePublished - Dec 1983

Fingerprint

Dive into the research topics of 'On universal locally finite groups'. Together they form a unique fingerprint.

Cite this