Multiplier groups of planar difference sets and a theorem of Kantor

Authors:
Chat Yin Ho and Alexander Pott

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

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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.

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DOI:
https://doi.org/10.1090/S0002-9939-1990-1017847-7

Article copyright:
© Copyright 1990
American Mathematical Society