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Quasi-endomorphisms in small stable groups

Published online by Cambridge University Press:  12 March 2014

Frank O. Wagner
Frank O. Wagner*
Affiliation:
Mathematisches Institut, Abteilung für Logik und Grundlagenforschung, Universität Freiburg, Albertstr, 23B, 79104 Freiburg, Deutschland, E-mail: frwagner@ibm.ruf.uni-freiburg.de
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Abstract

We generalise various properties of quasiendomorphisms from groups with regular generic to small abelian groups. In particular, for a small stable abelian group such that no infinite definable quotient is connected-by-finite, the ring of quasi-endomorphisms is locally finite. Under some additional assumptions, it decomposes modulo some nil ideal into a sum of finitely many matrix rings.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 3 , September 1993 , pp. 1044 - 1051
Copyright
Copyright © Association for Symbolic Logic 1993

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References

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