Archive for Mathematical Logic

, Volume 54, Issue 5–6, pp 571–586 | Cite as

Typical automorphism groups of finite nonrigid structures

  • Vera KoponenEmail author


We work with a finite relational vocabulary with at least one relation symbol with arity at least 2. Fix any integer m > 1. For almost all finite structures (labelled or unlabelled) such that at least m elements are moved by some automorphisms, the automorphism group is \({(\mathbb{Z}_2)^{i}}\) for some \({i \leq (m+1)/2}\); and if some relation symbol has arity at least 3, then the automorphism group is almost always \({\mathbb{Z}_{2}}\).


Finite model theory Limit law Random structure Automorphism group 

Mathematics Subject Classification

Primary 03C13 Secondary 60C05 20B25 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden

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