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DEFINABLY SIMPLE STABLE GROUPS WITH FINITARY GROUPS OF AUTOMORPHISMS

Published online by Cambridge University Press:  10 April 2019

ULLA KARHUMÄKI
ULLA KARHUMÄKI*
Affiliation:
SCHOOL OF MATHEMATICS UNIVERSITY OF MANCHESTER OXFORD ROAD, MANCHESTER M13 9PL, UKE-mail: ulla.karhumaki@manchester.ac.uk
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Abstract

We prove that infinite definably simple locally finite groups of finite centraliser dimension are simple groups of Lie type over locally finite fields. Then, we identify conditions on automorphisms of a stable group that make it resemble the Frobenius maps, and allow us to classify definably simple stable groups in the specific case when they admit such automorphisms.

Keywords

03C6020G99locally finite groupsstable groupsFrobenius maps
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 2 , June 2019 , pp. 704 - 712
Copyright
Copyright © The Association for Symbolic Logic 2019 

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