Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Finite projective planes and a question about primes


Author: Walter Feit
Journal: Proc. Amer. Math. Soc. 108 (1990), 561-564
MSC: Primary 51E15; Secondary 05B10, 51A35
DOI: https://doi.org/10.1090/S0002-9939-1990-1002157-4
MathSciNet review: 1002157
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ n$ be an even integer not divisible by 3. Suppose that $ p = {n^2} + n + 1$ is a prime and $ {2^{n + 1}} \equiv 1\left( {\bmod p} \right)$. The question is asked whether this can only occur if $ n$ is a power of 2. It is noted that an affirmative answer to this question implies that a finite projective plane with a flag transitive collineation group is Desarguesian.


References [Enhancements On Off] (What's this?)

  • [1] L.D. Baumert, Cyclic difference sets, Lecture Notes in Math. 182 Springer, New York, 1971. MR 0282863 (44:97)
  • [2] B. Gordon, W.H. Mills and L.R. Welch, Some new difference sets, Canad. J. Math 14 (1962), 614-625. MR 0146135 (26:3661)
  • [3] M. Hall, Jr., Combinatorial theory, Blaisdell, Waltham, Massachusetts (1967). MR 0224481 (37:80)
  • [4] W.M. Kantor, Primitive permutation groups of odd degree, and an application to finite projective planes, J. of Algebra 106 (1987), 15-45. MR 878466 (88b:20007)
  • [5] D. Jungnickel and K. Vedder, On the geometry of planar difference sets, European J. Combin. 5 (1984), 143-148. MR 753004 (85i:05047)
  • [6] H.A. Wilbrink, A note on planar difference sets, J. of Combin. Theory 38 (1985), 94-95. MR 773562 (86e:05015)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 51E15, 05B10, 51A35

Retrieve articles in all journals with MSC: 51E15, 05B10, 51A35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1002157-4
Keywords: Finite projective plane, flag transitive, prime
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society