A Freiheitssatz for Whitehead Graphs of One-Relator Groups with Small Cancellation

Abstract

In this work we study one-relator groups with a certain small cancellation condition. We focus on the following two general problems: the free subgroups of these groups, and what can be said on the automorphism group of these groups. Both problems are widely open. We introduce a graph-theoretical test which, if successful, implies that the subgroup under consideration is free. We also extend a result due to V. Shpilrain on automorphism groups of one-relator groups.

Key Words:

• Freiheitssatz
• One relator groups
• Small cancellation
• Whitehead graphs

2000 Mathematics Subject Classification:

• Primary 20E06, 20F05
• Secondary 20F06

ACKNOWLEDGMENT

I am grateful to the referee for his very useful comments which much improved the presentation of the article.

Notes

Communicated by M. Cohen.