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  • Currently known as: Glasgow Mathematical Journal Title history
    Proceedings of the Glasgow Mathematical Association, Volume 3, Issue 1
  • December 1956, pp. 38-44

Remarks on the Upper Centralc Series of a Group

  • D. H. McLain (a1)
  • DOI: http://dx.doi.org/10.1017/S2040618500033414
  • Published online: 01 May 2009
Abstract

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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1.R. Baer , Das Hyperzentrum einer Gruppe III, Math. Z., 59 (19531954), 296338.

2.R. Baer , Supersoluble groups, Proc. Amer. Math. Soc., 6 (1955), 1632.

5.F. Haimo , On the FC-chain of a group, Canad. Jour. Math., 5 (1953), 498511.

11.A. J. Weir , The Sylow p-subgroups of the general linear group over finite fields of characteristic p, Proc. Amer. Math. Soc., 6 (1955), 454464.

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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