Growth in finite simple groups of Lie type
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Tartalom: http://real.mtak.hu/44517/
Archívum: MTA Könyvtár
Gyűjtemény: Status = Published

Type = Article
Cím:
Growth in finite simple groups of Lie type
Létrehozó:
Pyber, László
SzabĂł, Endre
Kiadó:
American Mathematical Society
Dátum:
2016
Téma:
QA72 Algebra / algebra
Tartalmi leírás:
We prove that if $ L$ is a finite simple group of Lie type and $ A$ a set of generators of $ L$, then either $ A$ grows, i.e., $ vert A^3vert > vert Avert^(1+varepsilon )$ where $ varepsilon $ depends only on the Lie rank of $ L$, or $ A^3=L$. This implies that for simple groups of Lie type of bounded rank a well-known conjecture of Babai holds, i.e., the diameter of any Cayley graph is polylogarithmic. We also obtain new families of expanders.
A generalization of our proof yields the following. Let $ A$ be a finite subset of $ SL(n,mathbb(F))$, $ mathbb(F)$ an arbitrary field, satisfying $ big vert A^3big vertle mathcal (K)vert Avert$. Then $ A$ can be covered by $ mathcal (K)^m$, i.e., polynomially many, cosets of a virtually soluble subgroup of $ SL(n,mathbb(F))$ which is normalized by $ A$, where $ m$ depends on $ n$.
- See more at: http://www.ams.org/journals/jams/0000-000-00/S0894-0347-201...
Nyelv:
angol
magyar
Típus:
Article
PeerReviewed
info:eu-repo/semantics/article
Formátum:
text
text
Azonosító:
Pyber, László and Szabó, Endre (2016) Growth in finite simple groups of Lie type. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 29. pp. 95-146. ISSN 0894-0347
Kapcsolat:
MTMT:2829768; doi:10.1090/S0894-0347-2014-00821-3