Locally finite group

A group in which every finitely-generated subgroup is finite. Any locally finite group is a torsion group (cf. Periodic group), but not conversely (see 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 [3] (see Group with a finiteness condition). A locally finite group whose Abelian subgroups have finite rank (cf. Rank of a group) has itself finite rank and contains a locally solvable subgroup (cf. Locally solvable group) of finite index.

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