Journal of the London Mathematical Society



Notes and Papers

A STRUCTURAL PROPERTY CONCERNING ABSTRACT COMMENSURABILITY OF SUBGROUPS


R. I. GRIGORCHUK a1p1 and J. S. WILSON a2p2
a1 Steklov Mathematical Institute, Gubkina Street 8, Moscow 117966, Russia
a2 School of Mathematics and Statistics, University of Birmingham, Edgbaston, Birmingham B15 2TT

Article author query
grigorchuk r   [Google Scholar] 
wilson j   [Google Scholar] 
 

Abstract

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)

Maths Classification

20F10; 20E34 (primary); 20E08 (secondary).


Correspondence:
p1 Current address: Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA grigorch@math.tamu.edu
p2 Current address: Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB wilsonjs@maths.ox.ac.uk