The small index property of automorphism groups of ab-initio generic structures

Zaniar Ghadernezhad

The small index property of automorphism groups of ab-initio generic structures

Logic 2016-09-02 v2 Group Theory

Authors: Zaniar Ghadernezhad

Abstract

Suppose $M$ is a countable ab-initio (uncollapsed) generic structure which is obtained from a pre-dimension function with rational coefficients. We show that if $H$ is a subgroup of $\mbox{Aut}\left(M\right)$ with $\left[\mbox{Aut}\left(M\right):H\right]<2^{\aleph_{0}}$ , then there exists a finite set $A\subseteq M$ such that $\mbox{Aut}_{A}\left(M\right)\subseteq H$ . This shows that $\mbox{Aut}\left(M\right)$ has the small index property.

Keywords

ab-initio generic structures automorphism groups small index property pre-dimension function countable structures subgroup index rational coefficients

Cite

@article{arxiv.1510.00586,
  title  = {The small index property of automorphism groups of ab-initio generic structures},
  author = {Zaniar Ghadernezhad},
  journal= {arXiv preprint arXiv:1510.00586},
  year   = {2016}
}

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19 pages

The small index property of automorphism groups of ab-initio generic structures

Abstract

Keywords

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