# Locally solvable group

From Encyclopedia of Mathematics

A group in which every finitely-generated subgroup is solvable (see Finitely-generated group; Solvable group). The class of locally solvable groups is closed with respect to taking subgroups and homomorphic images, but it is not closed under extension.

A locally solvable torsion group is locally finite.

#### References

[1] | A.G. Kurosh, "The theory of groups" , 1–2 , Chelsea (1955–1956) (Translated from Russian) |

**How to Cite This Entry:**

Locally solvable group. A.L. Shmel'kin (originator),

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Locally_solvable_group&oldid=13816

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098