A Tits alternative for groups that are residually of bounded rank (Q1288488)

The authors continue their investigations of groups which are residually of bounded rank. Here they aim to prove analogues of the famous Tits alternative for linear groups. The main result is as follows. Theorem A: Let \(G\) be a group which is residually locally (soluble-by-finite) of rank \(r\). Then either \(G\) is locally (soluble-by-finite) or it contains a non-abelian free subgroup. The proof uses the classification of finite simple groups. Several other theorems of this type are proved.