Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-24T12:40:50.241Z Has data issue: false hasContentIssue false
  • English
  • Français

Partitioned groups and the additive structure of centralizer near-rings

Published online by Cambridge University Press:  20 January 2009

Martin R. Pettet
Martin R. Pettet
Affiliation:
Department of Mathematics, University of ToledoToledo, Ohio 43606
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 is a finite group and A is a group of automorphisms of G, the “centralizer” nearring C(A, G) consists of the identity-preserving maps from G to itself which commute with the action of A. The main concern of this paper will be with the additive structur of C(A, G) in the case that this near-ring is semisimple.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 27 , Issue 1 , February 1984 , pp. 47 - 56
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

REFERENCES

1.Dickson, L. E., Linear Groups: With an exposition of the Galois field theory, With an introduction by W. Magnus (Dover, New York, 1958).Google Scholar
2.Dieudonne, J., On the automorphisms of the classical groups. With a supplement by Loo-Keng Hua (Mem. Amer. Math. Soc. No. 2, 1951).Google Scholar
3.Gorenstein, D., Finite Groups (Harper and Row, New York, 1968).Google Scholar
4.Isaacs, I. M., Character Theory of Finite Groups (Academic Press, New York, 1976).Google Scholar
5.Kegel, O. H., Nicht-einfache Partitionen endlicher Gruppen, Arch. Math. 12 (1961), 170–175.CrossRefGoogle Scholar
6.Maxson, C. J. and Smith, K. C., The centralizer of a set of group automorphisms, Comm. Algebra 8 (1980), 211–230.CrossRefGoogle Scholar
7.Suzuki, M., On characterizations of linear groups, I, Trans. Amer. Math. Soc. 92 (1959), 191–219.Google Scholar
8.Suzuki, M., On a finite group with a partition, Arch. Math. 12 (1961), 241–254.CrossRefGoogle Scholar
9.Suzuki, M., On a class of doubly transitive groups, Ann. of Math. (2) 75 (1962), 105–145.CrossRefGoogle Scholar