The translation planes of order 49 and their automorphism groups
HTML articles powered by AMS MathViewer
- by C. Charnes and U. Dempwolff PDF
- Math. Comp. 67 (1998), 1207-1224 Request permission
Abstract:
Using isomorphism invariants, we enumerate the translation planes of order 49 and determine their automorphism groups.References
- A. Aho, B. W. Kernighan and P. J. Weinberger. The AWK Programming Language. Addison-Wesley, Reading, Mass., 1988.
- R. D. Baker and G. L. Ebert, Construction of two-dimensional flag-transitive planes, Geom. Dedicata 27 (1988), no. 1, 9–14. MR 950320, DOI 10.1007/BF00181610
- C. Charnes, Ph.D. thesis, Cambridge University, 1989.
- Chris Charnes, Quadratic matrices and the translation planes of order $5^2$, Coding theory, design theory, group theory (Burlington, VT, 1990) Wiley-Intersci. Publ., Wiley, New York, 1993, pp. 155–161. MR 1227127
- Chris Charnes, A pair of mutually polar translation planes, Ars Combin. 37 (1994), 121–128. MR 1282550
- C. Charnes and U. Dempwolff, Involutory homologies and translation planes of order 49. Abstracts Australian Mathematical Society Annual Conference, University of Wollongong, July 5-9, 1993.
- C. Charnes and U. Dempwolff, Spreads ovoids and $S_5$, Geom. Dedicata, 56 (1995), 129-143.
- J. H. Conway, P. B. Kleidman and R. A. Wilson, New families of ovoids in $O^+_8$. Geom. Dedicata, 26 (1988), 157-170.
- P. Dembowski, Finite Geometries. Springer-Verlag, Berlin, 1968.
- U. Dempwolff, Translation planes of order 27. Designs, Codes and Cryptography, 4 (1994), 105-121.
- G. Heimbeck, Translationsebenen der Ordnung 49 mit einer Quaternionengruppe von Dehnungen. Journal of Geometry, 44 (1992), 65-76.
- G. Heimbeck, Translationsebenen der Ordnung 49 mit Scherungen. Geom. Dedicata, 27 (1988), 87-100.
- U. Dempwolff and A. Reifart, The classification of the translation planes of order 16 I, Geom. Dedicata, 15 (1983), 137-153.
- H. Lüneburg, Translation Planes. Springer-Verlag, Berlin, New York, 1980.
- R. Mathon and G. Royle, The translation planes of order 49. Designs, Codes and Cryptography, 5 (1995), 57-72.
- M. Schönert et al., GAP Groups, Algorithms and Programming 3.3, Lehrstuhl D für Mathematik, RWTH Aachen, 1993.
- E. E. Shult, A sporadic ovoid in $\Omega ^+(8,7)$. Algebras, Groups and Geometries, 2 (1985), 495-513.
Additional Information
- C. Charnes
- Affiliation: Department of Computer Science University of Wollongong, FB Mathematik Universität Kaiserslautern
- Email: charnes@cs.uow.edu.au
- U. Dempwolff
- Affiliation: Department of Computer Science University of Wollongong, FB Mathematik Universität Kaiserslautern
- Email: dempwolff@mathematik.uni-kl.de
- Received by editor(s): July 3, 1995
- Received by editor(s) in revised form: April 23, 1997
- © Copyright 1998 American Mathematical Society
- Journal: Math. Comp. 67 (1998), 1207-1224
- MSC (1991): Primary 51E15, 68R05, 05B25
- DOI: https://doi.org/10.1090/S0025-5718-98-00961-2
- MathSciNet review: 1468940