Geodesic
QUASI-RANDOM PROFINITE GROUPS
Glasgow mathematical journal, Tome 57 (2015) no. 1, pp. 181-200

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DOI

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.
DOI : 10.1017/S0017089514000251
Mots-clés : 20P05, 20F, 20C33 
BARDESTANI, MOHAMMAD; MALLAHI-KARAI, KEIVAN. QUASI-RANDOM PROFINITE GROUPS. Glasgow mathematical journal, Tome 57 (2015) no. 1, pp. 181-200. doi: 10.1017/S0017089514000251
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     author = {BARDESTANI, MOHAMMAD and MALLAHI-KARAI, KEIVAN},
     title = {QUASI-RANDOM {PROFINITE} {GROUPS}},
     journal = {Glasgow mathematical journal},
     pages = {181--200},
     year = {2015},
     volume = {57},
     number = {1},
     doi = {10.1017/S0017089514000251},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089514000251/}
}
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