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QUASI-RANDOM PROFINITE GROUPS

Published online by Cambridge University Press:  22 December 2014

MOHAMMAD BARDESTANI  and
KEIVAN MALLAHI-KARAI
MOHAMMAD BARDESTANI
Affiliation:
Départment de Mathématiques et Statistique, Université de Montréal, CP 6128, succ. Centre-ville, Montréal, QC, CanadaH3C 3J7
KEIVAN MALLAHI-KARAI
Affiliation:
Jacobs University Bremen, Campus Ring I, 28759 Bremen, Germany e-mail: k.mallahikarai@jacobs-university.de
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Abstract

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Inspired by Gowers' seminal paper (W. T. Gowers, Comb. Probab. Comput.17(3) (2008), 363–387, we will investigate quasi-randomness for profinite groups. We will obtain bounds for the minimal degree of non-trivial representations of SLk(ℤ/(pnℤ)) and Sp2k(ℤ/(pnℤ)). Our method also delivers a lower bound for the minimal degree of a faithful representation of these groups. Using the suitable machinery from functional analysis, we establish exponential lower and upper bounds for the supremal measure of a product-free measurable subset of the profinite groups SLk(ℤp) and Sp2k(ℤp). We also obtain analogous bounds for a special subgroup of the automorphism group of a regular tree.

Keywords

20P0520F20C33
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 1 , January 2015 , pp. 181 - 200
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

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