Abstract
This paper consists essentially of a table showing for all 862 non-abelian groups G of order |G| ≤ 100 the order of the inner automorphism nearring (I(G), +, ∘) and the order of the commutator subgroup (I(G)’, +) of (I(G), +). The table was computed by using a program in GAP (Groups, Algorithms and Programming). The extensive calculations were done on a SUN-SPARCstation 20.
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
A. Fröhlich. The near-ring generated by the inner automorphisms of a finite simple group. J. London Math. Soc. 33 (1958), 95–107.
M. Hall, Jr., J. K. Senior. The groups of order 2n (n ≤ 6). The Macmillan Company. New York 1964.
B. Huppert. Endliche Gruppen I. Springer-Verlag. Berlin, Heidelberg, New York 1967.
R. Laue. Zur Konstruktion und Klassifikation endlicher auflösbarer Gruppen. Bayreuther Math. Schr. 9 (1982).
J. J. Malone. Endomorphism near-rings through the ages. In: Near-Rings and Near-Fields, Y. Fong et al. (eds.). Kluwer Academic Publishers. Dordrecht 1995, 31–44.
J. D. P. Meldrum. Near-rings and their links with groups. Research Notes in Mathematics 134. Pitman Adv. Publ. Program. Boston, London 1985.
J. Neubüser. Die Untergruppenverbände der Gruppen der Ordnungen ≤ 100 mit Ausnahme der Ordnungen 64 und 96. Habilitationsschrift, Universität Kiel 1967.
G. Saad, S.A. Syskin, M. J. Thomsen. Endomorphism nearrings on finite groups, a report. In: Near-Rings and Near-Fields, Y. Fong et al. (eds.). Kluwer Academic Publishers. Dordrecht 1995, 227–238.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Kluwer Academic Publishers
About this chapter
Cite this chapter
Saad, G., Syskin, S.A., Thomsen, M.J. (1997). The Inner Automorphism Nearrings I(G) on all Nonabelian Groups G of Order |G| ≤ 100. In: Saad, G., Thomsen, M.J. (eds) Nearrings, Nearfields and K-Loops. Mathematics and Its Applications, vol 426. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1481-0_31
Download citation
DOI: https://doi.org/10.1007/978-94-009-1481-0_31
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7163-5
Online ISBN: 978-94-009-1481-0
eBook Packages: Springer Book Archive