Baumslag-Solitar group

 $\langle b,t\mid t^{-1}b^{m}t=b^{n}\rangle$

for some non-zero integers $m$ and $n$.

These groups were studied by Baumslag and Solitar[1], who were interested in finding examples of finitely generated non-Hopfian (http://planetmath.org/HopfianGroup) groups. In particular, the group

 $\langle b,t\mid t^{-1}b^{2}t=b^{3}\rangle$

is non-Hopfian.

References

• 1 G. Baumslag, D. Solitar, Some two-generator one-relator non-Hopfian groups, Bull. Amer. Math. Soc., 68 (1962) 199–201. (This paper is http://projecteuclid.org/euclid.bams/1183524561available on-line from Project Euclid.)
• 2 D. J. Collins, http://eom.springer.de/b/b130070.htmBaumslag–Solitar group, in the Online Encyclopaedia of Mathematics.
Title Baumslag-Solitar group BaumslagSolitarGroup 2013-03-22 17:25:12 2013-03-22 17:25:12 yark (2760) yark (2760) 5 yark (2760) Definition msc 20F05 Solitar-Baumslag group