Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T06:24:07.799Z Has data issue: false hasContentIssue false
  • English
  • Français

Homomorphisms of sharply transitive projective planes

Published online by Cambridge University Press:  17 April 2009

Don Row
Don Row
Affiliation:
University of Tasmania, Hobart, Tasmania
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.

We construct projective planes having non-degenerate homomorphic images, the homomorphisms preserving certain sharply transitive collineation groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 4 , Issue 3 , June 1971 , pp. 361 - 366
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Hall, Marshall Jr, “Cyclic protective planes”, Duke Math. J. 14 (1947), 1079–1090.Google Scholar
[2]Hughes, D.R., “A note on difference sets”, Proc. Amer. Math. Soc. 6 (1955), 689–692.CrossRefGoogle Scholar
[3]Hughes, D.R., “On homomorphisms of projective planes”, Proc. Sympos. Appl. Math. 10, 45–52 (Amer. Math. Soc., Providence, Rhode Island, 1960).CrossRefGoogle Scholar
[4]Karzel, Helmut, “Bericht über projektive Inzidenzgruppen”, Jber. Deutsah. Math.-Verein. 67 (1961/1965), 58–92.Google Scholar
[5]Klingenberg, Wilhelm, “Projektive Geometrien mit Homomorphismus”, Math. Ann. 132 (1956), 180–200.CrossRefGoogle Scholar
[6]Row, Don, “A homomorphism theorem for projective planes”, Bull. Austral. Math. Soc. 4 (1971), 155–158.Google Scholar
[7]Singer, James, “A theorem in finite projective geometry and some applications to number theory”, Trans. Amer. Math. Soc. 43 (1938), 377–385.Google Scholar
[8]Skornyakov, L.A., “Projective planes” (Russian), Uspehi Matem. Nauk 6 (46) (1951), 112–154.Google Scholar