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FINITELY PRESENTED SUBGROUPS OF AUTOMATIC GROUPS AND THEIR ISOPERIMETRIC FUNCTIONS

Published online by Cambridge University Press:  01 October 1997

GILBERT BAUMSLAG ,
MARTIN R. BRIDSON ,
CHARLES F. MILLER III  and
HAMISH SHORT
GILBERT BAUMSLAG
Affiliation:
Department of Mathematics, City College of New York, Convent Avenue 138th Street, New York, New York 10031, USA
MARTIN R. BRIDSON
Affiliation:
Mathematical Institute, 24–29 St. Giles, Oxford OX1 3LB
CHARLES F. MILLER III
Affiliation:
Department of Mathematics, University of Melbourne, Parkville 3052, Australia
HAMISH SHORT
Affiliation:
U.R.A. 225, Centre de Mathématiques et d'Informatique, Université de Provence, F-13453 Marseille cedex 13, France
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Abstract

We describe a general technique for embedding certain amalgamated products into direct products. This technique provides us with a way of constructing a host of finitely presented subgroups of automatic groups which are not even asynchronously automatic. We can also arrange that such subgroups satisfy, at best, an exponential isoperimetric inequality.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 56 , Issue 2 , October 1997 , pp. 292 - 304
Copyright
The London Mathematical Society 1997

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Footnotes

This work was supported in part by NSF Grants no. 9103098 (first author) and no. 9203500 (second author).