caa a22 4500 386386110 CHVBK 20180307112058.0 cr unu---uuuuu 161130e198911 xx s 000 0 eng 10.1017/S0305004100068110 doi S0305004100068110 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100068110 Residually finite groups of finite rank [Elektronische Daten] The recent constructions, by Rips and Olshanskii, of infinite groups with all proper subgroups of prime order, and similar ‘monsters', show that even under the imposition of apparently very strong finiteness conditions, the structure of infinite groups can be rather weird. Thus it seems reasonable to impose the type of condition that enables us to apply the theory of finite groups. Two such conditions are local finiteness and residual finiteness, and here we are interested in the latter. Specifically, we consider residually finite groups of finite rank, where a group is said to have rank r, if all finitely generated subgroups of it can be generated by r elements. Recall that a group is said to be virtually of some property, if it has a subgroup of finite index with this property. We prove the following result: Theorem 1. A residually finite group of finite rank is virtually locally soluble. Copyright © Cambridge Philosophical Society 1989 Lubotzky Alexander Hebrew University, Jerusalem Mann Avinoam Hebrew University, Jerusalem Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 106/3(1989-11), 385-388 0305-0041 106:3<385 1989 106 PSP https://doi.org/10.1017/S0305004100068110 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100068110 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lubotzky Alexander Hebrew University, Jerusalem NATIONALLICENCE 700 1- Mann Avinoam Hebrew University, Jerusalem NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 106/3(1989-11), 385-388 0305-0041 106:3<385 1989 106 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge