Typical automorphism groups of finite nonrigid structures

Vera Koponen

Typical automorphism groups of finite nonrigid structures

Logic 2013-11-19 v2

Authors: Vera Koponen

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 $(Z_2)^i$ for some $i \leq (m+1)/2$ ; and if some relation symbol has arity at least 3, then the automorphism group is almost always $Z_2$ .

Keywords

automorphism groups group theory wreath product of groups

Cite

@article{arxiv.1310.6973,
  title  = {Typical automorphism groups of finite nonrigid structures},
  author = {Vera Koponen},
  journal= {arXiv preprint arXiv:1310.6973},
  year   = {2013}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1305.3097

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