Abstract
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 \({\mathbb{Z}_{2}}\).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ahlman O., Koponen V.: Limit laws and automorphism groups of random nonrigid structures. J. Log. Anal. 7(2), 1–53 (2015)
Dixon J.D., Mortimer B.: Permutation Groups. Springer, Berlin (1996)
Ebbinghaus H-D., Flum J.: Finite Model Theory. 2nd edn. Springer, Berlin (1999)
Erdős P., Rényi A.: Asymmetric graphs. Acta Math. Acad. Sci. Hung. 14, 295–315 (1963)
Fagin R.: The number of finite relational structures. Discr. Math. 19, 17–21 (1977)
Ford G.W., Uhlenbeck G.E.: Combinatorial problems in the theory of graphs. IV. Proc. Natl. Acad. Sci. 43, 163–167 (1957)
Harary F.: Note on Carnap’s relational asymptotic relative frequencies. J. Symb. Log. 23, 257–260 (1958)
Oberschelp, W.: Strukturzahlen in endlichen Relationssystemen. In: H. A. Schmidt (eds.) Contributions to Mathematical Logic, pp. 199–213. Proceedings of 1966 Logic Colloquium, North-Holland (1968)
Rothmaler P.: Introduction to Model Theory. Taylor & Francis, London (2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Koponen, V. Typical automorphism groups of finite nonrigid structures. Arch. Math. Logic 54, 571–586 (2015). https://doi.org/10.1007/s00153-015-0428-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00153-015-0428-9