# Betti group

From Encyclopedia of Mathematics

In a broad sense, the same as a homology group; in a narrow sense, the Betti group is the free part of the homology group with as domain of coefficients the group $\mathbf Z$ of integers, if this homology group is finitely generated. Named after E. Betti (1823–1892).

#### References

[1] | H. Seifert, W. Threlfall, "A textbook of topology" , Acad. Press (1980) (Translated from German) |

[2] | P.S. Aleksandrov, "An introduction to homological dimension theory and general combinatorial topology" , Moscow (1975) (In Russian) |

#### Comments

#### References

[a1] | E.H. Spanier, "Algebraic topology" , McGraw-Hill (1966) |

**How to Cite This Entry:**

Betti group.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Betti_group&oldid=32657

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article