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Mathematics > Group Theory

arXiv:0710.0437 (math)
[Submitted on 2 Oct 2007 (v1), last revised 10 Mar 2008 (this version, v2)]

Title:Connectivity of the Product Replacement Graph of Simple Groups of Bounded Lie Rank

Authors:Nir Avni, Shelly Garion
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Abstract: The Product Replacement Algorithm is a practical algorithm for generating random elements of a finite group. The algorithm can be described as a random walk on a graph whose vertices are the generating k-tuples of the group (for a fixed integer k).
We show that there is a function c(r) such that for any finite simple group of Lie type, with Lie rank r, the product replacement graph of the generating k-tuples is connected for any k > c(r).
The proof uses results of Larsen and Pink and does not rely on the classification of finite simple groups.
Comments: v2 Minor changes, some explanations added
Subjects: Group Theory (math.GR)
MSC classes: 20D06 (Primary); 20G40, 20D60 (Secondary)
Cite as: arXiv:0710.0437 [math.GR]
  (or arXiv:0710.0437v2 [math.GR] for this version)
  https://doi.org/10.48550/arXiv.0710.0437
Journal reference: J. Algebra 320 (2008), 945-960
Related DOI: https://doi.org/10.1016/j.jalgebra.2008.03.005

Submission history

From: Nir Avni [view email]
[v1] Tue, 2 Oct 2007 04:03:15 UTC (15 KB)
[v2] Mon, 10 Mar 2008 00:57:54 UTC (16 KB)
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