Finitely presented simple groups and products of trees

Marc Burger; Shahar Mozes

doi:10.1016/S0764-4442(97)86938-8

Finitely presented simple groups and products of trees

Marc Burger^*, Shahar Mozes

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

80 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	747-752
Number of pages	6
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	324
Issue number	7
DOIs	https://doi.org/10.1016/S0764-4442(97)86938-8
State	Published - 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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title = "Finitely presented simple groups and products of trees",

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

author = "Marc Burger and Shahar Mozes",

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{\textquoteright}s theorem: PROPOSITIO5N. - Lrt G < hut, I be (I closed, ioc~dl~ x-tmnsitivr .suhgroup and (r. 3-t) a continuous unitary representation of{\textquoteright} G with 710 r7oti,7t{\textquoteright}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{\textquoteright}, x H2. HI x Pz} and thus N c nl,CH,X~i2f!()hP{\textquoteright}; 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{\textquoteright}. 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).",

year = "1997",

month = apr,

doi = "10.1016/S0764-4442(97)86938-8",

language = "אנגלית",

volume = "324",

pages = "747--752",

journal = "Comptes Rendus de l'Academie des Sciences - Series I: Mathematics",

issn = "0764-4442",

publisher = "Academie des sciences",

number = "7",

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AU - Burger, Marc

AU - Mozes, Shahar

N1 - 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).

PY - 1997/4

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Finitely presented simple groups and products of trees

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