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Hypercentre

From Encyclopedia of Mathematics
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A member of the upper central series of a group . The first hypercentre is the centre of the group (cf. Centre of a group); if all , , are known, then if is a limit ordinal number; is the complete pre-image of the centre of the quotient group if is a non-limit ordinal number. The hypercentres of a group are locally nilpotent.


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References

[a1] D.J.S. Robinson, "Finiteness condition and generalized soluble groups" , 1–2 , Springer (1972)
How to Cite This Entry:
Hypercentre. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hypercentre&oldid=36025
This article was adapted from an original article by V.M. Kopytov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article