Propriétés résiduelles des groupes, et méthodes probabilistes

László Pyber; Aner Shalev

doi:10.1016/S0764-4442(01)02044-4

Propriétés résiduelles des groupes, et méthodes probabilistes

Translated title of the contribution: Residual properties of groups and probabilistic methods

László Pyber^*, Aner Shalev

^*Corresponding author for this work

Einstein Institute of Mathematics

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

3 Scopus citations

Abstract

We outline a probabilistic approach to the solution of a number of problems concerning residual properties of infinite groups. This approach gives rise to a new and short proof of a well known conjecture of Magnus. It also yields new results on residual properties of the modular group PSL₂(Z) and of other free products of finite groups. Similar ideas can be used to show the existence of finitely generated dense free subgroups in various profinite groups, and yield an analogue of the Tits alternative for profinite completions of linear groups.

Translated title of the contribution	Residual properties of groups and probabilistic methods
Original language	French
Pages (from-to)	275-278
Number of pages	4
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	333
Issue number	4
DOIs	https://doi.org/10.1016/S0764-4442(01)02044-4
State	Published - 15 Aug 2001

Bibliographical note

Funding Information:
*Research partially supported by grant OTKA T22925 for L.P., and a grant from the Israel Science Foundation for A.S.

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10.1016/S0764-4442(01)02044-4

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AB - We outline a probabilistic approach to the solution of a number of problems concerning residual properties of infinite groups. This approach gives rise to a new and short proof of a well known conjecture of Magnus. It also yields new results on residual properties of the modular group PSL2(Z) and of other free products of finite groups. Similar ideas can be used to show the existence of finitely generated dense free subgroups in various profinite groups, and yield an analogue of the Tits alternative for profinite completions of linear groups.

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Propriétés résiduelles des groupes, et méthodes probabilistes

Abstract

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