Finitely presented simple groups and products of trees

Marc Burger*, Shahar Mozes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

78 Scopus citations


We construct lattices in Aut Tn × Aut Tm which are finitely presented, torsion free, simple groups.

Original languageAmerican English
Pages (from-to)747-752
Number of pages6
JournalComptes Rendus de l'Academie des Sciences - Series I: Mathematics
Issue number7
StatePublished - Apr 1997

Bibliographical note

Funding Information:
is that if ~1E HI x Hz generates an unbounded subgroup A = (!q), then A acts x HT. This follows from the following analogue of Howe-Moore’s theorem: PROPOSITIO5N. - Lrt G < hut, I be (I closed, ioc~dl~ x-tmnsitivr .suhgroup and (r. 3-t) a continuous unitary representation of’ G with 710 r7oti,7t’ro CJcm-)invwimt rwtors. Then all matrix c~o@icients of T owlish ut i$itzit!.. Returning to the sketch of the proof of theorem 4, we conclude that N acts trivially on HI x Hz/t) where () E {PI x I:. I’, x H2. HI x Pz} and thus N c nl,CH,X~i2f!()hP’; as both HI, Hz are topologically simple. the latter group is ( x 0. HI x c or o x Hz. If for example N c HI x C, then prl(:V)aprl(l?) = 1!1, and hence 11: = f’. QED. Rcscarch partially supported by Fonda National Suisse de la Recherche Scientitique, Israel Academy of Sciences. and by the Edmund Landau Center for research in Mathematical Analysis supported by the Minerva Foundation (Federal Republic of Germany).


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