Geodesic
Reflections on the residual finiteness of one-relator groups
Gilbert Baumslag1 ; Charles F. Miller III2 ; Douglas Troeger1
1The City College of New York, United States
2University of Melbourne, Melbourne, Australia
Groups, geometry, and dynamics, Tome 1 (2007) no. 3, pp. 209-219

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DOI

Let G = < a, b, ... | r = 1 > be a one-relator group equipped with at least two generators. For all w which do not commute with r in the ambient free group on the generators a, b, ..., the groups G(r,w) = < a,b, ... | r r w = r 2 > are not residually finite and have the same finite images as G. The existence of this family of one-relator groups which are not residually finite reinforces what is becoming more obvious with time, that one-relator groups can be extremely complicated. This not only serves to underline the complexity of one-relator groups but provides us with the opportunity to raise a number of problems about these groups in the hope that they will stimulate further work on the conjugacy and isomorphism problems for one-relator groups as a whole.
DOI : 10.4171/ggd/11
Classification : 20-XX, 00-XX
Mots-clés : One-relator group, residually finite, isomorphism problem

Gilbert Baumslag  1   ; Charles F. Miller III  2   ; Douglas Troeger  1

1 The City College of New York, United States
2 University of Melbourne, Melbourne, Australia 
Gilbert Baumslag; Charles F. Miller III; Douglas Troeger. Reflections on the residual finiteness of one-relator groups. Groups, geometry, and dynamics, Tome 1 (2007) no. 3, pp. 209-219. doi: 10.4171/ggd/11
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