Geodesic
Remarks on the Upper Centralc Series of a Group
Glasgow mathematical journal, Tome 2 (1956) no. 1, pp. 38-44

Voir la notice de l'article provenant de la source Cambridge University Press

Following, for example, Kurošs [8], we define the (transfinite) upper central series of a group G to be the seriessuch 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. 
McLain, D. H. Remarks on the Upper Centralc Series of a Group. Glasgow mathematical journal, Tome 2 (1956) no. 1, pp. 38-44. doi: 10.1017/S2040618500033414
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[1] 1.Baer, R., Das Hyperzentrum einer Gruppe III, Math. Z., 59 (1953–1954), 296–338. Google Scholar | DOI

[2] 2.Baer, R., Supersoluble groups, Proc. Amer. Math. Soc., 6 (1955), 16–32. Google Scholar | DOI

[3] 3.Birkhoff, G., Lattice theory (Amer. Math. Soc, 1948). Google Scholar

[4] 4.Duguid, A. M. and McLain, D. H., FC-soluble and FC-nilpotent groups, Proc. Comb. Phil.Soc., 52 (1956), 391–398. Google Scholar | DOI

[5] 5.Haimo, F., On the FC-chain of a group, Canad. Jour. Math., 5 (1953), 498–511. Google Scholar | DOI

[6] 6.Hall, P., A contribution to the theory of groups of prime power order, Proc. Lond. Math.Soc., 36 (1933), 29–95. Google Scholar

[7] 7.Hall, P., Finiteness conditions for soluble groups, Proc. Lond. Math. Soc., (3) 4 (1954), 419–436. Google Scholar

[8] 8.Kurošs, A. G., Theory of groups, (Chelsean, 1955). Google Scholar

[9] 9.Mal'cev, A. I., Generalised nilpotent algebras and their associated groups, Mat. Sbornik N.S., 25 (1949), 347–366. (in Russian). Google Scholar

[10] 10.McLain, D. H., On locally nilpotent groups, Proc. Camb. Phil. Soc., 52 (1956), 5–11. Google Scholar | DOI

[11] 11.Weir, A. J., The Sylow p-subgroups of the general linear group over finite fields of characteristic p, Proc. Amer. Math. Soc., 6 (1955), 454–464. Google Scholar

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