Locally solvable group
From Encyclopedia of Mathematics
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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.
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
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