Author:
ABDOLLAHI ALIREZA,MALEKAN MEISAM SOLEIMANI
Abstract
Abstract
The following question is proposed by Martino, Tointon, Valiunas and Ventura in [4, question 1·20]:
Let G be a compact group, and suppose that
\[\mathcal{N}_k(G) = \{(x_1,\dots,x_{k+1}) \in G^{k+1} \;|\; [x_1,\dots, x_{k+1}] = 1\}\]
has positive Haar measure in
$G^{k+1}$
. Does G have an open k-step nilpotent subgroup?
We give a positive answer for
$k = 2$
.
Publisher
Cambridge University Press (CUP)
Reference5 articles.
1. The probability that x and y commute in a compact group
2. [2] Hewitt, E. and Ross, K. A. . Abstract Harmonic Analysis: Structure and Analysis for Compact Groups Analysis on Locally Compact Abelian Groups. Grundlehren Math. Wiss. (Springer, Berlin, 2013).
3. [5] Soleimani Malekan, M. , Abdollahi, A. and Ebrahimi, M. . Compact groups with many elements of bounded order. J. Group Theory 23, no. 6 (2020), 991–998.
4. [4] Martino, A. , Tointon, M. C. H. , Valiunas, M. and Ventura, E. . Probabilistic nilpotence in infinite groups. to appear in Israel J. Math.
Cited by
1 articles.
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