Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-28T15:18:43.431Z Has data issue: false hasContentIssue false
  • English
  • Français

Frattini classes of saturated formations of finite groups

Published online by Cambridge University Press:  17 April 2009

Peter Förster
Peter Förster
Affiliation:
Mathematics Research Section, IAS, The Australian National University Canberra, ACT 2601, Australia
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.

We study the following question: given any local formation of finite groups, do there exist maximal local subformations? An answer is given by providing a local definition of the intersection of all maximal local subformations.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 2 , October 1990 , pp. 267 - 286
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Barnes, D.W. and Kegel, O.H., ‘Gaschütz functors on finite soluble groups’, Math. Z. 94 (1966), 134–142.CrossRefGoogle Scholar
[2]Bryant, R.M., Bryce, R.A. and Hartley, B., ‘The formation generated by a finite group.’, Bull. Austral. Math. Soc. 2 (1970), 347–357.CrossRefGoogle Scholar
[3]Förster, P., ‘Closure operations for Schunck classes and formations of finite solvable groups’, Math. Proc. Cambridge Philos. Soc. 85 (1979), 253–259.CrossRefGoogle Scholar
[4]Förster, P., ‘Projektive Klassen endlicher Gruppen I. Schunck- und Gaschützklassen’, Math. Z. 186 (1984), 149–178.CrossRefGoogle Scholar
[5]Förster, P., ‘Projektive Klassen endlicher Gruppen IIa. Gesättigte Formationen: Ein allgemeiner Satz vom Gaschütz-Lubeseder-Baer-Typ’, Publ. Sec. Mat. Univ. Autònoma Barcelona 29 (1985), 39–76.Google Scholar
[6]Förster, P., ‘An elementary proof of Lubeseder’s theorem’, Arch. Math. 52 (1989), 417–419.CrossRefGoogle Scholar
[7]Förster, P. and Salomon, E., ‘Local definitions of local homomorphs and formations of finite groups’, Bull. Austral. Math. Soc. 31 (1985), 5–34.CrossRefGoogle Scholar
[8]Hall, P., ‘On non-strictly simple groups’, Proc. Cambridge Philos. Soc. 59 (1963), 531–553.CrossRefGoogle Scholar
[9]Herzfeld, U.C., ‘Frattiniklassen und maximale Teilklassen, insbesondere zu Formationen endlicher Gruppen’, Dissertation, Mainz (1985).Google Scholar
[10]Herzfeld, U.C., ‘Frattiniklassen und maximale Teilklassen, insbesondere zu Formationen endlicher Gruppen’, Dissertation, Mainz (1986).Google Scholar
[11]Herzfeld, U.C., ‘Frattiniclasses and maximal subclasses, in particular of formations of finite groups’, J. Algebra 117 (1988), 93–98.CrossRefGoogle Scholar
[12]Herzfeld, U.C., ‘Frattiniclasses of formations of finite groups’, Boll. Un. Mat. Ital. (7) 2-B (1988), 601–611.Google Scholar
[13]Huppert, B., Endliche Gruppen I (Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
[14]Kovács, L.G. and Newman, M.F., ‘On critical groups’, J. Auatral. Math. Soc. 6 (1966), 237–250.Google Scholar
[15]Neumann, H., Varieties of groups (Springer-Verlag, Berlin,-Heidelberg, New York, 1967).CrossRefGoogle Scholar
[16]Salomon, E., ‘Local definability of formation products’, Comm. Algebra (to appear).Google Scholar