Baumslag-Solitar group

A Baumslag-Solitar group is a group with presentation

\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
Canonical name	BaumslagSolitarGroup
Date of creation	2013-03-22 17:25:12
Last modified on	2013-03-22 17:25:12
Owner	yark (2760)
Last modified by	yark (2760)
Numerical id	5
Author	yark (2760)
Entry type	Definition
Classification	msc 20F05
Synonym	Solitar-Baumslag group