Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-06T07:13:33.604Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite p-groups with Homogyclic Central Factors

Published online by Cambridge University Press:  20 November 2018

Joseph A. Gallian
Joseph A. Gallian*
Affiliation:
University of Minnesota, Duluth, Duluth, Minnesota
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.

If G has nilpotence class c(G) = c, let G = L1(G) > L2 (G)> . . . > Lc+1(G) = 1 and 1 = Z0(G) < Z1(G) < . . . < Zc(G) = G denote the lower central series and upper central series of G respectively. When there is no possibility of confusion we use Li for Li(G) and Zi for Zi(G). Throughout the paper we assume that G is a finite p-group of class greater than two. Let B (c, pr) denote the collection of all G of class c for which Li/Li+i is cyclic of order pr for i = 2, . . . , c and UC(c, pr) the collection of all G of class c for which Zi/Zi-1 is cyclic of order pr for i = 1, . . . , c – 1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 3 , June 1974 , pp. 636 - 643
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Baumslag, G. and Blackburn, N., Groups with cyclic upper central factors, Proc. London Math. Soc. 10 (1960), 531–544.Google Scholar
2. Blackburn, N., On a special class of p-groups, Acta Math. 100 (1958), 45–92.Google Scholar
3. Gallian, J., Two-step centralizers infinite p-groups, Ph.D. dissertation, University of Notre Dame, 1971.Google Scholar
4. Gorenstein, D., Finite groups (Harper & Row, New York, 1968).Google Scholar
5. Huppert, B., Endliche Gruppen I (Springer-Verlag, Berlin, 1967).Google Scholar