scholarly journals Profinite invariants of arithmetic groups

2020 ◽  
Vol 8 ◽  
Author(s):  
Holger Kammeyer ◽  
Steffen Kionke ◽  
Jean Raimbault ◽  
Roman Sauer
Keyword(s):  
Euler Characteristic ◽  
Finite Groups ◽  
Congruence Subgroup ◽  
Arithmetic Groups ◽  
Profinite Completion ◽  
Residually Finite ◽  
Residually Finite Groups ◽  
Congruence Subgroup Property

Abstract We prove that the sign of the Euler characteristic of arithmetic groups with the congruence subgroup property is determined by the profinite completion. In contrast, we construct examples showing that this is not true for the Euler characteristic itself and that the sign of the Euler characteristic is not profinite among general residually finite groups of type F. Our methods imply similar results for $\ell^2$ -torsion as well as a strong profiniteness statement for Novikov–Shubin invariants.

A PROBABILISTIC ZETA FUNCTION FOR ARITHMETIC GROUPS

2005 ◽  
Vol 15 (05n06) ◽  
pp. 1053-1059 ◽  
Author(s):  
AVINOAM MANN
Keyword(s):  
Analytic Function ◽  
Zeta Function ◽  
Half Plane ◽  
Congruence Subgroup ◽  
Profinite Group ◽  
Arithmetic Groups ◽  
Finitely Generated ◽  
Profinite Completion ◽  
Random Elements ◽  
Congruence Subgroup Property

A profinite group G is positively finitely generated (PFG) if for some k, the probability P(G,k) that k random elements generate G is positive. It was conjectured that if G is PFG, then the function P(G,k) can be interpolated to an analytic function defined in some right half-plane. Here that conjecture is formulated more precisely, and verified for (the profinite completion of) arithmetic groups satisfying the congruence subgroup property.

scholarly journals The profinite completion of multi-EGS groups

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Anitha Thillaisundaram ◽  
Jone Uria-Albizuri
Keyword(s):  
Congruence Subgroup ◽  
Profinite Completion ◽  
Congruence Subgroup Property

AbstractThe class of multi-EGS groups is a generalisation of the well-known Grigorchuk–Gupta–Sidki (GGS-)groups. Here we classify branch multi-EGS groups with the congruence subgroup property and determine the profinite completion of all branch multi-EGS groups. Additionally, our results show that branch multi-EGS groups are just infinite.

scholarly journals On Groups of Automorphisms of Residually Finite Groups

2000 ◽  
Vol 231 (2) ◽  
pp. 561-573
Author(s):  
Ulderico Dardano ◽  
Bettina Eick ◽  
Martin Menth
Keyword(s):  
Finite Groups ◽  
Residually Finite ◽  
Residually Finite Groups ◽  
Groups Of Automorphisms

scholarly journals An uncountable family of finitely generated residually finite groups

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hip Kuen Chong ◽  
Daniel T. Wise
Keyword(s):  
Free Group ◽  
Finite Groups ◽  
Finitely Generated ◽  
Residually Finite ◽  
Uncountable Family ◽  
Residually Finite Groups ◽  
Rank 2

Abstract We study a family of finitely generated residually finite groups. These groups are doubles F 2 * H F 2 F_{2}*_{H}F_{2} of a rank-2 free group F 2 F_{2} along an infinitely generated subgroup 𝐻. Varying 𝐻 yields uncountably many groups up to isomorphism.

Actions and Invariants of Residually Finite Groups: Asymptotic Methods

2010 ◽  
pp. 2335-2391
Author(s):  
Miklós Abért ◽  
Damien Gaboriau ◽  
Fritz Grunewald
Keyword(s):  
Finite Groups ◽  
Asymptotic Methods ◽  
Residually Finite ◽  
Residually Finite Groups

scholarly journals Hydra group doubles are not residually finite

2016 ◽  
Vol 8 (2) ◽  
Author(s):  
Kristen Pueschel
Keyword(s):  
Finite Groups ◽  
Recursive Function ◽  
Dehn Functions ◽  
Residually Finite ◽  
Residually Finite Groups ◽  
Finitely Presented

AbstractIn 2013, Kharlampovich, Myasnikov, and Sapir constructed the first examples of finitely presented residually finite groups with large Dehn functions. Given any recursive function

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