Finitely generated simple sharply 2-transitive groups

We construct the first examples of infinite sharply 2-transitive groups which are finitely generated. Moreover, we construct such a group that has Kazhdan property (T), is simple, has exactly four conjugacy classes and we show that this number is as small as possible.

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Bibliographic Details
Published in:Compositio mathematica 2024-08, Vol.160 (8), p.1941-1957
Main Authors: André, Simon, Guirardel, Vincent
Format: Article
Language:English
Subjects:
Group Theory
Mathematics
Prime numbers
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Description
Summary:We construct the first examples of infinite sharply 2-transitive groups which are finitely generated. Moreover, we construct such a group that has Kazhdan property (T), is simple, has exactly four conjugacy classes and we show that this number is as small as possible.
ISSN:0010-437X
1570-5846
DOI:10.1112/S0010437X24007358