Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2025-01-03T18:20:45.188Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite groups which are the product of two nilpotent subgroups

Published online by Cambridge University Press:  17 April 2009

Fletcher Gross
Fletcher Gross
Affiliation:
Department of Mathematics, The University of Utah, Salt Lake City, Utah, USA.
Rights & Permissions [Opens in a new window]

Abstract

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.

Suppose G = AB where G is a finite group and A and B are nilpotent subgroups. It is proved that the derived length of G modulo its Frattini subgroup is at most the sum of the classes of A and B. An upper bound for the derived length of G in terms of the derived lengths of A and B also is obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 9 , Issue 2 , October 1973 , pp. 267 - 274
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Gaschütz, Wolfgang, “Zur Theorie der endlichen auflösbaren Gruppen”, Math. Z. 80 (1963), 300–305.Google Scholar
[2]Gross, Fletcher, “The 2-length of groups whose Sylow 2-groups are of exponent 4”, J. Algebra 2 (1965), 312–314.Google Scholar
[3]Hall, P. and Higman, Graham, “On the p–length of p-soluble groups and reduction theorems for Burnside's problem”, Proc. London Math. Soc. (3) 6 (1956), 1–42.Google Scholar
[4]Itô, Noboru, “Über das Produkt von zwei abelschen Gruppen”, Math. Z. 62 (1955), 400–401.CrossRefGoogle Scholar
[5]Kegel, Otto H., “Produkte nilpotenter Gruppen”, Arah. Math. 12 (1961), 90–93.Google Scholar
[6]Wielandt, Helmut, “Über das Produkt paarweise vertauschbarer nilpotenter Gruppen”, Math. Z. 55 (1951), 1–7.CrossRefGoogle Scholar