Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T11:59:28.651Z Has data issue: false hasContentIssue false
  • English
  • Français

Some generalizations of normal series in infinite groups

Published online by Cambridge University Press:  09 April 2009

Richard E. Phillips
Richard E. Phillips
Affiliation:
Department of MathematicsMichigan State University, U.S.A.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we are concerned with certain generalizations of subnormal and ascendent (transfinitely subnormal) subgroups of a group. A subgroup A of a group G is called f-ascendent in G if there is a well ordered ascending complete series of subgroups of G, where for all α < λ, either Gα ⊲ Gα+1 or [Gα+1: Gα] < ∞. If such a series has finite length, A is called F-subnormal in G.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 4 , December 1972 , pp. 496 - 502
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Baer, R., ‘Abzahlbar erkennbare grouppentheoretische Eigenshaften’, Math. Z. 79 (1962), 344–363.CrossRefGoogle Scholar
[2]Bear, R., ‘Nilgruppen’, Math. Z. 62 (1955), 402–437.Google Scholar
[3]Gruenberg, K., ‘The engel elements of a solvable group’, III, J. of Math. 3 (1959), 151–168.Google Scholar
[4]Heineken, H. and Mohamad, I., ‘A group with trivial center satisfying the normalizer condition’, J. of Algebra 10 (1968), 368–376.Google Scholar
[5]Kurosh, A. G., The theory of groups, Vol. II, (Chelsea, New York, 1956).Google Scholar
[6]McLain, D. H., ‘Remarks on the upper central series of a group’, Proc. Glascow Math. Assoc. 3 (1956), 38–44.Google Scholar
[7]Phillips, R. E. and Combrink, C. R., ‘A note on subsolvable groups’, Math. Z., 92 (1966), 349–352.CrossRefGoogle Scholar
[8]Plotkin, B. I., ‘Radical groups’, Transl. Amer. Math. Soc. 17 (series 2) (1961), 9–28.Google Scholar
[9]Robinson, D. S., Infinite soluble and nilpotent groups (Queen Mary College Math. Notes, London.)Google Scholar
[10]Zassenhaus, H., The theory of groups (2nd Ed., Chelsea New York, 1956).Google Scholar
[11]Scott, W. R., Group theory Prentice-Hall, Englewood Cliffs, N. J. (1965).Google Scholar