Higher rank arithmetic groups which are not invariably generated

It was conjectured in [KLS14] that for arithmetic groups, Invariable Generation is equivalent to the Congruence Subgroup Property. In view of the famous Serre conjecture this would imply that higher rank arithmetic groups are invariably generated. In this paper we prove that some higher rank arithme...

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Bibliographic Details
Published in:arXiv.org 2021-02
Main Authors: Gelander, Tsachik, Chen Meiri
Format: Article
Language:English
Subjects:
Arithmetic
Subgroups
Online Access:Get full text
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Summary:It was conjectured in [KLS14] that for arithmetic groups, Invariable Generation is equivalent to the Congruence Subgroup Property. In view of the famous Serre conjecture this would imply that higher rank arithmetic groups are invariably generated. In this paper we prove that some higher rank arithmetic groups are not invariably generated.
ISSN:2331-8422