# Baumslag-Solitar group

A *Baumslag-Solitar group* is a group with presentation^{}

$$\u27e8b,t\mid {t}^{-1}{b}^{m}t={b}^{n}\u27e9$$ |

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

$$\u27e8b,t\mid {t}^{-1}{b}^{2}t={b}^{3}\u27e9$$ |

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 |