locally finite group
(Kaplansky) If is a group such that for a normal subgroup of , and are locally finite, then is locally finite.
A solvable torsion group is locally finite. To see this, let be a composition series for . We have that each is normal in and the factor group is abelian. Because is a torsion group, so is the factor group . Clearly an abelian torsion group is locally finite. By applying the fact in the previous paragraph for each step in the composition series, we see that must be locally finite.
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- 3 I. Kaplansky, Notes on Ring Theory, University of Chicago, Math Lecture Notes, (1965).
- 4 C. Procesi, On the Burnside problem, Journal of Algebra, 4 (1966) 421-426.
|Title||locally finite group|
|Date of creation||2013-03-22 14:18:44|
|Last modified on||2013-03-22 14:18:44|
|Last modified by||CWoo (3771)|