A STRUCTURAL PROPERTY CONCERNING ABSTRACT COMMENSURABILITY OF SUBGROUPS
Further properties of a group $\Gamma$ introduced by the first author in 1980 (sometimes called the first Grigorchuk group) are established. These are notably that any two infinite finitely generated subgroups of $\Gamma$ have isomorphic subgroups of finite index and that the generalized word problem for $\Gamma$ is soluble.(Received September 10 2002)
(Revised March 10 2003)
20F10; 20E34 (primary); 20E08 (secondary).
p1 Current address: Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA [email protected]
p2 Current address: Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB [email protected]