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Torsion group

From Encyclopedia of Mathematics
Revision as of 20:43, 29 April 2012 by Ulf Rehmann (talk | contribs) (moved Periodic group to Torsion group: more common name)
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A group in which every element has finite order. Any periodic Abelian group splits into a direct sum of primary groups with respect to distinct prime numbers. See Burnside problem on periodic groups for finiteness conditions of periodic groups.


Comments

A periodic group is also called a torsion group. For any group , its torsion subgroup is defined by . It is a normal subgroup and the quotient is the torsion-free quotient group of . Both and are functors.

References

[a1] A.G. Kurosh, "The theory of groups" , 1–2 , Chelsea (1955–1956) (Translated from Russian)
[a2] P. Hall, "The theory of groups" , Macmillan (1959) pp. Chapt. 10
[a3] D.J.S. Robinson, "Finiteness condition and generalized soluble groups" , I , Springer (1972)
How to Cite This Entry:
Torsion group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Torsion_group&oldid=25719
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article