View source for Locally finite group

A group in which every finitely-generated subgroup is finite. Any locally finite group is a torsion group (cf. [[Periodic group|Periodic group]]), but not conversely (see [[Burnside problem|Burnside problem]]). An extension of a locally finite group by a locally finite group is again a locally finite group. Every locally finite group with the minimum condition for subgroups (and even for Abelian subgroups) has an Abelian subgroup of finite index [[#References|[3]]] (see [[Group with a finiteness condition|Group with a finiteness condition]]). A locally finite group whose Abelian subgroups have finite rank (cf. [[Rank of a group|Rank of a group]]) has itself finite rank and contains a locally solvable subgroup (cf. [[Locally solvable group|Locally solvable group]]) of finite index.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  A.G. Kurosh,   "The theory of groups" , '''1–2''' , Chelsea  (1955–1956)  (Translated from Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  S.N. Chernikov,   "Finiteness conditions in general group theory"  ''Uspekhi Mat. Nauk'' , '''14''' :  5  (1959)  pp. 45–96  (In Russian)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  V.P. Shunkov,   "On locally finite groups with a minimality condition for Abelian subgroups"  ''Algebra and Logic'' , '''9''' :  5  (1970)  pp. 350–370  ''Algebra i Logika'' , '''9''' :  5  (1970)  pp. 579–615</TD></TR><TR><TD valign="top">[4]</TD> <TD valign="top">  V.P. Shunkov,   "On locally finite groups of finite rank"  ''Algebra and Logic'' , '''10''' :  2  (1971)  pp. 127–142  ''Algebra i Logika'' , '''10''' :  2  (1971)  pp. 199–225</TD></TR></table>