Locally solvable group

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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.


[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:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098