Abstract
Fitting functors have been introduced as a generalization of injectors and radicals for Fitting classes of finite (soluble) groups. This paper provides definitions and properties of certain types of Fitting functors which resemble injectors and radicals for Fitting classes with additional closure properties, most prominently subgroup- or quotient-closed Fitting classes and Fischer classes.
Similar content being viewed by others
References
Beidleman, J. C., Brewster, B., Hauck, P.: Fittingfunktoren in endlichen auflösbaren Gruppen I. Math. Z.182, 359–384 (1983).
Beidleman, J. C., Brewster, B., Hauck, P.: Fitting functors in finite solvable groups II. Math. Proc. Camb. Phil. Soc.101, 37–55 (1987).
Beidleman, J. C., Gállego, M. P.: Conjugate π-normally embedded Fitting functors. Rend. Semi. Mat. Univ. Padova80, 65–82 (1988).
Chambers, G.:p-normally embedded subgroups of finite soluble groups. J. Algebra16, 442–455 (1970).
Dark, R. S.: Some examples in the theory of injectors of finite soluble groups. Math. Z.127, 145–156 (1972).
Hartley, B.: On Fischer's dualization of formation theory. Proc. London Math. Soc. (3)19, 193–207 (1969).
Hawkes, T. O.: A Fitting class construction. Math. Proc. Camb. Phil. Soc.80, 437–446 (1976).
Lockett, F. P.: On the theory of Fitting classes of finite soluble groups. Ph. D. thesis. University of Warwick 1971.
Lockett, F. P.: On the theory of Fitting classes of finite soluble groups. Math. Z.131, 103–115 (1973).
Lockett, F. P.: The Fitting class ℱ* Math. Z.137, 131–136 (1974).
Müller, K.: Fittingklassen mit zusätzlichen Abschlußeigenschaften. Arch. Math.50, 19–24 (1988).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Beidleman, J.C., Hauck, P. Closure properties for fitting functors. Monatshefte für Mathematik 108, 1–22 (1989). https://doi.org/10.1007/BF01300063
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01300063