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We describe a new class of groups of Burnside type, by giving a procedure transforming an arbitrary non-free minimal action of the dihedral group on a Cantor set into an orbit-equivalent action of an infinite finitely generated periodic group. We show that if the associated Schreier graphs are linearly repetitive, then the group is of intermediate growth. In particular, this gives first examples of simple groups of intermediate growth.
@article{10_4007_annals_2018_187_3_2,
author = {Volodymyr Nekrashevych},
title = {Palindromic subshifts and simple periodic groups of intermediate growth},
journal = {Annals of mathematics},
pages = {667--719},
publisher = {mathdoc},
volume = {187},
number = {3},
year = {2018},
doi = {10.4007/annals.2018.187.3.2},
mrnumber = {3779956},
zbl = {06854655},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2018.187.3.2/}
}
TY - JOUR AU - Volodymyr Nekrashevych TI - Palindromic subshifts and simple periodic groups of intermediate growth JO - Annals of mathematics PY - 2018 SP - 667 EP - 719 VL - 187 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2018.187.3.2/ DO - 10.4007/annals.2018.187.3.2 LA - en ID - 10_4007_annals_2018_187_3_2 ER -
%0 Journal Article %A Volodymyr Nekrashevych %T Palindromic subshifts and simple periodic groups of intermediate growth %J Annals of mathematics %D 2018 %P 667-719 %V 187 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2018.187.3.2/ %R 10.4007/annals.2018.187.3.2 %G en %F 10_4007_annals_2018_187_3_2
Volodymyr Nekrashevych. Palindromic subshifts and simple periodic groups of intermediate growth. Annals of mathematics, Tome 187 (2018) no. 3, pp. 667-719. doi: 10.4007/annals.2018.187.3.2
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