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Growth in Groups and Graph Isomorphism Now

Total Cost €


EC-Contrib. €






Project "GROGandGIN" data sheet

The following table provides information about the project.


Organization address
address: REALTANODA UTCA 13-15
city: Budapest
postcode: 1053

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Hungary [HU]
 Total cost 1˙965˙340 €
 EC max contribution 1˙965˙340 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-ADG
 Funding Scheme ERC-ADG
 Starting year 2017
 Duration (year-month-day) from 2017-08-01   to  2022-07-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

'In recent years there has been spectacular progress in studying growth in groups. A central result in this new area, obtained by Pyber-Szabo' (with a similar result proved by Breuillard-Green-Tao), shows that powers of generating subsets of finite simple groups of 'bounded dimension' grow fast. Extending this Product Theorem Szabo' and the PI also proved a weaker version of a conjecture of Helfgott-Lindenstrauss. The Product Theorem has deep consequences in the study of groups, number theory and random walks. A central open question of the area is to remove the dependence on dimension in our Product Theorem. The PI formulated a new Conjecture, as a step forward. The way to further progress is via combining techniques from asymptotic group theory and probability theory. It is from this perspective that the current GROGandGIN proposal addresses issues concerning random walks. We examine how recent probabilistic arguments for random walks in the symmetric group may be transferred to matrix groups. While the first results in the subject of growth concern matrix groups we see an evolving theory of growth in permutation groups. This relies on earlier work of Babai and the PI which aims at finding proofs which do not use the Classification of Finite Simple Groups (CFSG). Similarly, Babai's famous Quasipolynomial Graph Isomorphism Algorithm builds on ideas from CFSG-free proofs due to him. The PI has recently removed CFSG from the analysis of Babai's algorithm. Our method goes 'halfway' towards removing CFSG from proofs of growth results for permutation groups, currently a major open problem. The GROGandGIN initiative plans to improve various other parts of Babai's paper, working with several people who look at it from different angles, with an eye towards obtaining a Polynomial Graph Isomorphism algorithm. The GROGandGIN team will also study growth in Lie groups since the theory of random walks in Lie groups has been revitalised using analogues of our Product Theorem.'


year authors and title journal last update
List of publications.
2019 Zoltán Halasi, Attila Maróti, Gabriel Navarro, Pham Huu Tiep
Irreducible induction and nilpotent subgroups in finite groups
published pages: , ISSN: 0021-8693, DOI: 10.1016/j.jalgebra.2019.05.009
Journal of Algebra 2020-04-15
2019 Attila Guld
\"FInite subgroups of the birational automorphism group are \"\"almost\"\" nilpotent\"
published pages: , ISSN: , DOI:
2020 Hülya Duyan, Zoltán Halasi, Károly Podoski
Random bases for coprime linear groups
published pages: 133-157, ISSN: 1433-5883, DOI: 10.1515//jgth-2019-0043
Journal of Group Theory 23/1 2020-04-15
2020 Zoltán Halasi
Diameter of Cayley graphs of SL(n,p) with generating sets containing a transvection
published pages: , ISSN: , DOI:
2020 Daniel di Benedetto, József Solymosi, Ethan White
On the directions determined by a Cartesian product in an affine Galois plane
published pages: , ISSN: , DOI:
2020 Attila Maróti, Iulian I. Simion
Bounding the number of classes of a finite group in terms of a prime
published pages: , ISSN: 1433-5883, DOI: 10.1515/jgth-2019-0144
Journal of Group Theory 0/0 2020-04-15
2019 Imre Ruzsa, George Shakan, József Solymosi, Endre Szemerédi
On distinct consecutive differences
published pages: , ISSN: , DOI:
2020 Alireza Abdollahi, Majid Arezoomand, Gareth Tracey
On finite totally 2-closed groups
published pages: , ISSN: , DOI:
2018 Zoltan Halasi, Attila Maroti, Laszlo Pyber, Youming Xiao
An improved diameter bound for finite simple groups of Lie type
published pages: , ISSN: , DOI:
submitted to the Bulletin of the London Mathematical Society 2020-04-15
2019 Zoltán Halasi, Martin W. Liebeck, Attila Maróti
Base sizes of primitive groups: Bounds with explicit constants
published pages: 16-43, ISSN: 0021-8693, DOI: 10.1016/j.jalgebra.2018.10.043
Journal of Algebra 521 2020-04-15
2018 Attila Guld
Boundedness properties of automorphsm groups of forms of flag varieties
published pages: , ISSN: , DOI:
submitted to Transformation Groups 2020-04-15
2019 József Solymosi, Ching Wong
The Brown-Erdős-Sós conjecture in finite abelian groups
published pages: , ISSN: , DOI:
submitted to Discrete Applied Mathematics 2020-04-15
2019 Ambrus Pál, Endre Szabó
The fibration method over real function fields
published pages: , ISSN: , DOI:
submitted to the Journal of the AMS 2020-04-15
2019 Gabor Kun, Andreas Thom
Inapproximability of actions and Kazhdan\'s property (T)
published pages: , ISSN: , DOI:
to be submitted to the Transactions of the AMS 2020-04-15
2019 Nick Gill, Laszlo Pyber, Endre Szabo
A generalization of a theorem of Rodgers and Saxl for simple groups of bounded rank
published pages: , ISSN: , DOI:
submitted to the Bulletin of the London Mathematical Society 2020-04-15
2019 Victor Bovdi, Thomas Breuer, Attila Maróti
Finite simple groups with few Galois orbits on conjugacy classes
published pages: , ISSN: , DOI:
submitted to the Canadian Mathematical Bulletin 2020-04-15
2019 Orit E. Raz, József Solymosi
Dense graphs have rigid parts
published pages: , ISSN: , DOI:
to be submitted to COMBINATORICA 2020-04-15
2019 David Szabo
Special p-groups acting on compact manifolds
published pages: , ISSN: , DOI:
to be submitted to the Transactions of the AMS 2020-04-15

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