Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-14T22:03:35.187Z Has data issue: false hasContentIssue false
  • English
  • Français

On non-strictly simple groups

Published online by Cambridge University Press:  24 October 2008

P. Hall
P. Hall
Affiliation:
King's College, Cambridge
Get access Rights & Permissions [Opens in a new window]

Extract

Ascending series. Let G be a group and λ an ordinal number. An ascending series of G of type λ is a set of subgroups Gα of G, defined for all α ≤ λ, and such that (i) G0 = 1, Gλ = G; (ii)Gα is a proper normal subgroup of Gα+1 for all α < λ (iii) for all limit ordinals μ ≤ λ.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 3 , July 1963 , pp. 531 - 553
Copyright
Copyright © Cambridge Philosophical Society 1963

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Plotkin, B. I.Generalized soluble and generalized nilpotent groups. Uspehi Mat. Nauk (N.S.), 13 (1958), 89–172;Google Scholar
American Math. Soc. Translations, (2), 17 (1961), 29–117.Google Scholar
(2)Kurosh, A. G.Theory of groups, vol. II, trans. Hirsch, K. A. (Chelsea; New York, 1956).Google Scholar
(3)Hall, P.Wreath powers and characteristically simple groups. Proc. Cambridge Philos. Soc. 58 (1962), 170–184.CrossRefGoogle Scholar
(4)Plotkin, B. I.Radical groups. Mat. Sbornik. (N.S.), 37 (79) (1955), 507–526;Google Scholar
American Math. Soc. Translations, (2), 17 (1961), 9–29.CrossRefGoogle Scholar
(5)Chehata, C. G.An algebraically simple ordered group. Proc. London Math Soc. (3), 2 (1952), 183–197.CrossRefGoogle Scholar
(6)Iwasawa, K.On linearly ordered groups. J. Math. Soc. Japan, 1 (1949), 1–9.Google Scholar
(7)McLain, D. H.A characteristically simple group. Proc. Cambridge Philos. Soc. 50 (1954), 641–642.CrossRefGoogle Scholar
(8)Schmidt, O.Infinite solvable groups. Mat. Sbornik. 17 (1945), 145–162.Google Scholar
(9)Hall, P.The Frattini subgroups of finitely generated groups. Proc. London Math. Soc. (3), 11 (1961), 327–352.CrossRefGoogle Scholar
(10)McLain, D. H.Finiteness conditions in locally soluble groups. J. London Math. Soc. 34 (1959), 101–107.CrossRefGoogle Scholar
(11)Gruenberg, K.The Engel elements of a soluble group. Illinois J. Math. 3(1959), 151–167.CrossRefGoogle Scholar
(12)Baer, R.über Nil-gruppen. Math. Z. 62 (1955), 402–437.CrossRefGoogle Scholar
(13)Sierpiński, W.Cardinal and ordinal numbers (Warsaw, 1958).Google Scholar