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|
|Number of pages||4|
|Journal||Comptes Rendus de l'Academie des Sciences - Series I: Mathematics|
|State||Published - 15 Aug 2001|
Bibliographical noteFunding Information:
*Research partially supported by grant OTKA T22925 for L.P., and a grant from the Israel Science Foundation for A.S.