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A STRUCTURAL PROPERTY CONCERNING ABSTRACT COMMENSURABILITY OF SUBGROUPS

Published online by Cambridge University Press:  17 November 2003

R. I. GRIGORCHUK  and
J. S. WILSON
R. I. GRIGORCHUK
Affiliation:
Steklov Mathematical Institute, Gubkina Street 8, Moscow 117966, Russia Current address: Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, [email protected]
J. S. WILSON
Affiliation:
School of Mathematics and Statistics, University of Birmingham, Edgbaston, Birmingham B15 2TT Current address: Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB [email protected]
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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.

Keywords

20F1020E34 (primary)20E08 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 68 , Issue 3 , December 2003 , pp. 671 - 682
Copyright
The London Mathematical Society 2003

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