# Zaniar Ghadernezhad's research while affiliated with Institute for Research in Fundamental Sciences (IPM) and other places

## Publications (7)

Preprint
Full-text available
We classify all group topologies coarser than the topology of stabilizers of finite sets in the case of automorphism groups of countable free-homogeneous structures, Urysohn space and Urysohn sphere, among other related results.
Article
Full-text available
We prove a version of a small index property theorem for strong amalgamation classes. Our result builds on an earlier theorem by Lascar and Shelah (in their case, for saturated models of uncountable first-order theories). We then study versions of the small index property for various non-elementary classes. In particular, we obtain the small index...
Article
In this paper we prove that the automorphism groups of certain countable generic structures are not amenable. For doing that, we first prove the existence of particular matrices that do not satisfy the convex Ramsey condition. For a pair of elements in a smooth class, we introduce the property of forming a free-pseudoplane in the generic structure....
Article
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...
Article
We investigate correspondences between extreme amenability and amenability of automorphism groups of Fra\"iss\'e-Hrushovski generic structures that are obtained from smooth classes, and their Ramsey type properties of their smooth classes, similar to Kechris, Pestov and Todorcevic, and Tatch Moore. In particular, we focus on some Fra\"iss\'e-Hrusho...
Article
We show that the automorphism groups of certain countable structures obtained using the Hrushovski amalgamation method are simple groups. The structures we consider are the 'uncollapsed' structures of infinite Morley rank obtained by the ab initio construction and the (unstable) omega-categorical pseudoplanes. The simplicity of the automorphism gro...
Article
We show that there are simple groups with a spherical BN-pair of rank 2 which are non-Moufang and hence not of algebraic origin.

## Citations

... As indicated in the introduction, the practical use of Theorem 1.13 is so far limited. There are promising exceptions, as the papers by Gadhernezhad, Khalilian and Pourmahdian [GKP18], and by Etesami and Gadhernezhad [EG17], do make use of it to prove that certain automorphism groups of the form Aut(F), where F is a so-called Hrushovski structure, are not amenable. Nevertheless, there is presently no significant instance where Theorem 1.13 can be used to prove that some group is amenable. ...
... Acknowledgements: Several of the results given here appear in the PhD thesis of the Second Author [5] with a slightly different presentation. Work on the paper was completed whilst the Authors were participating in the trimester programme 'Universality and Homogeneity' at the Hausdorff Institute for Mathematics, Bonn. ...
... As indicated in the introduction, the practical use of Theorem 1.13 is so far limited. There are promising exceptions, as the papers by Gadhernezhad, Khalilian and Pourmahdian [GKP18], and by Etesami and Gadhernezhad [EG17], do make use of it to prove that certain automorphism groups of the form Aut(F), where F is a so-called Hrushovski structure, are not amenable. Nevertheless, there is presently no significant instance where Theorem 1.13 can be used to prove that some group is amenable. ...
... (Anbo and Ikeda [2010], Aref'ev [1995], Baldwin [1994], [1995], [2002], [2003], Baldwin and Holland [2000], [2001], [2003], [2004], Baldwin and Itai [1994], Baldwin and Shelah [1998], Baudisch [2009], [1995], Baudisch, Hils, Martin-Pizarro, and Wagner [2009], Baudisch, Martin-Pizarro, and Ziegler [2006], [2007a], [2007b], Baudisch and Pillay [2000], Ealy and Onshuus [2014], Evans [1997d], [2001], [2002], [2004], [2005], Evans and Ferreira [2011], [2012], Evans, Ghadernezhad, and Tent [2016], Evans and Pantano [2002], (B. Poizat) [1989], Hasson [2007], [2008], Hasson and Hils [2006], Hasson and Hrushovski [2007], Herwig [1991], [1995b], Holland [1995], [1997], [1999], Hrushovski [1988], [1992b], [1993b], [1998], Ikeda [2001], [2002], [2005], [2012], Ikeda and Kikyo [2012], Ikeda, Kikyo, and Tsuboi [2009], Kueker and Laskowski [1992], Pillay and Tsuboi [1997], Poizat [1999], [2001], [2002], Pourmahdian [2002], [2003a], [2003b], [2004], Pourmahdian and Wagner [2006], Sudoplatov [2005], [2006], [2007b], [2007a], [2015], Tent [2000], Tsuboi [2001b], [2001a], Verbovsky [2006], Verbovsky and Yoneda [2003], Wagner [1994], [2009], Ziegler [2008], [2013], Zilber [2003], [2004], [2005], [2006]); relation to random structures (Baldwin [1997], [2000], [2006], Baldwin and Mazzucco [2006], Baldwin and Shelah [1997], Baldwin and Shi [1996], Beyarslan [2006], [2010], Beyarslan and Hrushovski [2012], Debonis and Nesin [1998], Dolan and Lynch [1993], Lynch [1980], [1985], [1990], [1992], [1994], [1997], [1998], [2005]). ...
... If M is an algebraically closed field of characteristic zero (and of countably infinite transcendence rank), then it can be shown that all non-identity automorphisms are unbounded, so in this case G is simple (note that acl(∅) is the algebraic closure of the prime field). Lascar's result has recently been used in [4] to give examples of simple groups with BN -pairs which do not arise from algebraic groups. ...
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