GGS-groups: Order of congruence quotients and Hausdorff dimension
Authors:
Gustavo A. Fernández-Alcober and Amaia Zugadi-Reizabal
Journal:
Trans. Amer. Math. Soc. 366 (2014), 1993-2017
MSC (2010):
Primary 20E08
DOI:
https://doi.org/10.1090/S0002-9947-2013-05908-9
Published electronically:
October 16, 2013
MathSciNet review:
3152720
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: If is a GGS-group defined over a
-adic tree, where
is an odd prime, we calculate the order of the congruence quotients
for every
. If
is defined by the vector
, the determination of the order of
is split into three cases, according to whether
is non-symmetric, non-constant symmetric, or constant. The formulas that we obtain only depend on
,
, and the rank of the circulant matrix whose first row is
. As a consequence of these formulas, we also obtain the Hausdorff dimension of the closures of all GGS-groups over the
-adic tree.
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Additional Information
Gustavo A. Fernández-Alcober
Affiliation:
Matematikaren eta Zientzia Esperimentalen Didaktika Saila, Euskal Herriko Unibertsitatea UPV/EHU, 48080 Bilbao, Spain
Email:
gustavo.fernandez@ehu.es
Amaia Zugadi-Reizabal
Affiliation:
Matematikaren eta Zientzia Esperimentalen Didaktika Saila, Euskal Herriko Unibertsitatea UPV/EHU, 48080 Bilbao, Spain
Email:
amaia.zugadi@ehu.es
DOI:
https://doi.org/10.1090/S0002-9947-2013-05908-9
Received by editor(s):
August 17, 2011
Received by editor(s) in revised form:
June 29, 2012
Published electronically:
October 16, 2013
Additional Notes:
The authors were supported by the Spanish Government, grant MTM2008-06680-C02-02, partly with FEDER funds, and by the Basque Government, grant IT-460-10
The second author was also supported by grant BFI07.95 of the Basque Government
Article copyright:
© Copyright 2013
American Mathematical Society