Multiplier groups of planar difference sets and a theorem of Kantor
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- by Chat Yin Ho and Alexander Pott PDF
- Proc. Amer. Math. Soc. 109 (1990), 803-808 Request permission
Abstract:
A recent result of W. Kantor followed by a work of W. Feit has rekindled interest in the longstanding conjecture of finite cyclic planes. In this paper we prove that the order of the multiplier group equals the odd part of the order of the automorphism group of a Singer group if and only if the order of the plane is 2, 3, or 8. This yields another proof for Feit’s result mentioned above.References
- Leonard D. Baumert, Cyclic difference sets, Lecture Notes in Mathematics, Vol. 182, Springer-Verlag, Berlin-New York, 1971. MR 0282863
- Walter Feit, Finite projective planes and a question about primes, Proc. Amer. Math. Soc. 108 (1990), no. 2, 561–564. MR 1002157, DOI 10.1090/S0002-9939-1990-1002157-4
- Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
- Chat Y. Ho, On multiplier groups of finite cyclic planes, J. Algebra 122 (1989), no. 1, 250–259. MR 994947, DOI 10.1016/0021-8693(89)90249-4
- Daniel R. Hughes and Fred C. Piper, Projective planes, Graduate Texts in Mathematics, Vol. 6, Springer-Verlag, New York-Berlin, 1973. MR 0333959
- Dieter Jungnickel and Klaus Vedder, On the geometry of planar difference sets, European J. Combin. 5 (1984), no. 2, 143–148. MR 753004, DOI 10.1016/S0195-6698(84)80028-1
- William M. Kantor, Primitive permutation groups of odd degree, and an application to finite projective planes, J. Algebra 106 (1987), no. 1, 15–45. MR 878466, DOI 10.1016/0021-8693(87)90019-6
- Udo Ott, Endliche zyklische Ebenen, Math. Z. 144 (1975), no. 3, 195–215 (German). MR 380619, DOI 10.1007/BF01214135
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 803-808
- MSC: Primary 05B10; Secondary 11T15
- DOI: https://doi.org/10.1090/S0002-9939-1990-1017847-7
- MathSciNet review: 1017847