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Remarks on the Upper Centralc Series of a Group

Published online by Cambridge University Press:  18 May 2009

D. H. McLain
D. H. McLain
Affiliation:
The University Glasgow
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Following, for example, Kurošs [8], we define the (transfinite) upper central series of a group G to be the series

such that Zα + 1/Za is the centre of G/Zα, and if β is a limit ordinal, then If α is the least ordinal for which Zα =Zα+1=…, then we say that the upper central series has length α, and that Zα= His the hypercentre of G. As usual, we call G nilpotent if Zn= Gfor some finite n.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 3 , Issue 1 , December 1956 , pp. 38 - 44
Copyright
Copyright © Glasgow Mathematical Journal Trust 1956

References

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