Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-17T15:58:12.001Z Has data issue: false hasContentIssue false
  • English
  • Français

On the fitting core of a formation

Published online by Cambridge University Press:  17 April 2009

J. C. Beidleman  and
H. Heineken
J. C. Beidleman
Affiliation:
Department of Mathematics, University of Kentucky, Lexington KY 40506-0017, United States of America e-mail: clark@ms.uky.edu
H. Heineken
Affiliation:
Mathematisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany e-mail: Heineken@mathematik.uni-wurzburg.de
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.

Dedicated to the memory of Bernhard H. Neumann

Not often is a formation also a Fitting class. In this article groups are exhibited that are contained in a given saturated formation and that do not lead out of this formation by forming normal products with other groups of it. This generalises a result of Cossey on T-groups and supersolvable groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 1 , August 2003 , pp. 107 - 112
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Agrawal, R.K., ‘Finite groups whose subnormal subgroups permute with all Sylow subgroups’ Proc. Amer. Math. Soc. 47 (1975), 77–83.CrossRefGoogle Scholar
[2]Cossey, J., ‘Finite groups generated by subnormal T-groups’, Glasgow Math. J. 37 (1995), 363–371.CrossRefGoogle Scholar
[3]Dickson, L.E., Linear groups with an exposition of the Galois field theory (Dover Publications, New York, 1958).Google Scholar
[4]Doerk, K. and Hawkes, T., Finite soluble groups, de Gruyter Expositions in Mathematics 4 (de Gruyter and Co., Berlin, 1992).CrossRefGoogle Scholar
[5]Huppert, B., Endliche Gruppen I (Springer-Verlag, Berlin and New York, 1967).CrossRefGoogle Scholar