Abstract
Let G be a group. The structure of the centralizer near-ring M E (G) = {f: G → G | fσ = σf for every σ ∈ End G} is investigated for the cases in which G is a finitely generated abelian, characteristically simple, symmetric or generalized quaternion group.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. A. Cannon, Centralizer Near-Rings Determined by End G, Doctoral Dissertation, Texas A&M University, to appear.
J. R. Clay, Nearrings: Geneses and Applications, Oxford Science Publ., Oxford, 1992.
Y. Fong and J. D. P. Meldrum, Endomorphism Near-Rings of a Direct Sum of Isomorphic Finite Simple Nonabelian Groups, Near-Rings and Near-Fields ed. G. Betsch, North-Holland, Amsterdam, 1987, 73–78.
D. Gorenstein, Finite Groups, Harper & Row, New York, 1968.
J. J. Malone, Generalized Quaternion Groups and Distributively Generated Near-Rings, Proc. Edinburgh Math. Soc., 18 (1973), 235–238.
C. J. Maxson, M. R. Pettet and K. C. Smith, On Semisimple Rings that are Centralizer Near-Rings, Pacific J. Math., 101 (1981), 451–461.
C. J. Maxson and K. C. Smith, The Centralizer of a Set of Group Automorphisms, Comm. Alg., 8 (1980), 211–230.
C. J. Maxson and K. C. Smith, Centralizer Near-Rings Determined by Local Rings, Houston J. Math., 11 (1985), 355–366.
G. Pilz, Near-Rings, North Holland/American Elsevier, Amsterdam, second, revised edition, 1983.
W. R. Scott, Group Theory, Dover, New York, 1987.
M. Suzuki, Group Theory I, Springer-Verlag, 1982.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Cannon, G.A. (1995). Centralizer Near-Rings Determined by End g . In: Fong, Y., Bell, H.E., Ke, WF., Mason, G., Pilz, G. (eds) Near-Rings and Near-Fields. Mathematics and Its Applications, vol 336. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0359-6_10
Download citation
DOI: https://doi.org/10.1007/978-94-011-0359-6_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4160-7
Online ISBN: 978-94-011-0359-6
eBook Packages: Springer Book Archive