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ASCENDING HNN EXTENSIONS OF FINITELY GENERATED FREE GROUPS ARE HOPFIAN

Published online by Cambridge University Press:  14 June 2001

ROSS GEOGHEGAN ,
MICHAEL L. MIHALIK ,
MARK SAPIR  and
DANIEL T. WISE
ROSS GEOGHEGAN
Affiliation:
Dept. of Math., SUNY, Binghamton, NY 13902, USA; [email protected]
MICHAEL L. MIHALIK
Affiliation:
Dept. of Math., Vanderbilt University, Nashville, TN 37240, USA; [email protected]
MARK SAPIR
Affiliation:
Dept. of Math., Vanderbilt University, Nashville, TN 37240, USA; [email protected]
DANIEL T. WISE
Affiliation:
Dept. of Math., Cornell University, Ithaca, NY 14853, USA; [email protected]
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Abstract

It is shown that every ascending HNN extension of a finitely generated free group is Hopfian. An important ingredient in the proof is that under certain hypotheses on the group H, if G is an ascending HNN extension of H, then cd(G) = cd(H) + 1.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 3 , May 2001 , pp. 292 - 298
Copyright
© The London Mathematical Society 2001

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