Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T16:17:39.179Z Has data issue: false hasContentIssue false
  • English
  • Français

SEMIFIELDS ARISING FROM IRREDUCIBLE SEMILINEAR TRANSFORMATIONS

Part of: Finite geometry and special incidence structures General nonassociative rings

Published online by Cambridge University Press:  01 December 2008

WILLIAM M. KANTOR  and
ROBERT A. LIEBLER
WILLIAM M. KANTOR*
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97403, USA (email: kantor@math.uoregon.edu)
ROBERT A. LIEBLER
Affiliation:
Department of Mathematics, Colorado State University, Fort Collins, CO 80523, USA (email: liebler@math.colostate.edu)
*
✉For correspondence; e-mail: kantor@math.uoregon.edu
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.

A construction of finite semifield planes of order n using irreducible semilinear transformations on a finite vector space of size n is shown to produce fewer than different nondesarguesian planes.

Keywords

finite projective planessemifieldsemilinear transformation

MSC classification

Secondary: 51E15: Affine and projective planes 17A35: Division algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 85 , Issue 3 , December 2008 , pp. 333 - 339
Copyright
Copyright © Australian Mathematical Society 2009

References

[1]Dembowski, P., Finite Geometries (Springer, Berlin, 1968).CrossRefGoogle Scholar
[2]Dempwolff, U., ‘Normalformen semilinearer operatoren’, Math. Semesterber. 46 (1999), 205–214.CrossRefGoogle Scholar
[3]Dempwolff, U., Private communication, 2008.Google Scholar
[4]Jacobson, N., ‘Pseudo-linear transformations’, Ann. Math. 38 (1943), 484–507.CrossRefGoogle Scholar
[5]Jha, V. and Johnson, N. L., ‘An analog of the Albert–Knuth theorem on the orders of finite semifields, and a complete solution to Cofman’s subplane problem’, Algebras Groups Geom. 6 (1989), 1–35.Google Scholar
[6]Kantor, W. M., ‘Finite semifields’, in: Finite Geometries, Groups, and Computation, Proc. Conf., Pingree Park, CO, September 2005 (eds. A. Hulpke et al.) (de Gruyter, Berlin, 2006), pp. 103–114.CrossRefGoogle Scholar
[7]Knuth, D. E., ‘Finite semifields and projective planes’, J. Algebra 2 (1965), 182–217.CrossRefGoogle Scholar