Geodesic
Groups with property (T) and many alternating group quotients
Laurent Bartholdi1 orcid ; Martin Kassabov2 orcid
1Université Claude Bernard Lyon 1, Villeurbanne, France
2Cornell University, Ithaca, USA
Groups, geometry, and dynamics, Tome 19 (2025) no. 2, pp. 647-660

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DOI

We prove that, for the free algebra over a sufficiently rich operad O, a large subgroup of its group of tame automorphisms has Kazhdan’s property (T). We deduce that there exists a group with property (T) that maps onto large powers of alternating groups.
DOI : 10.4171/ggd/892
Classification : 22D55, 08A35, 17A36
Mots-clés : Kazhdan’s property T, tame algebra automorphisms, generation of powers of symmetric groups, operads

Laurent Bartholdi  1   ; Martin Kassabov  2

1 Université Claude Bernard Lyon 1, Villeurbanne, France
2 Cornell University, Ithaca, USA 
Laurent Bartholdi; Martin Kassabov. Groups with property (T) and many alternating group quotients. Groups, geometry, and dynamics, Tome 19 (2025) no. 2, pp. 647-660. doi: 10.4171/ggd/892
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     title = {Groups with property {(T)} and many alternating group~quotients},
     journal = {Groups, geometry, and dynamics},
     pages = {647--660},
     year = {2025},
     volume = {19},
     number = {2},
     doi = {10.4171/ggd/892},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/892/}
}
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