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New Flag-Transitive Affine Planes of Even Order

โœ Scribed by William M. Kantor; Michael E. Williams

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
522 KB
Volume
74
Category
Article
ISSN
0097-3165

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๐Ÿ“œ SIMILAR VOLUMES

A Trace Conjecture and Flag-Transitive A
A Trace Conjecture and Flag-Transitive Affine Planes
โœ R.D. Baker; G.L. Ebert; K.H. Leung; Q. Xiang ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 127 KB

For any odd prime power q, all (q 2 &q+1)th roots of unity clearly lie in the extension field F q 6 of the Galois field F q of q elements. It is easily shown that none of these roots of unity have trace &2, and the only such roots of trace &3 must be primitive cube roots of unity which do not belong

Cyclic affine planes of even order
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โœ K.T. Arasu ๐Ÿ“‚ Article ๐Ÿ“… 1989 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 446 KB

In this paper, we prove the following theorem: Suppose there exists a cyclic afhne plane of even order n. Then (a) either n = 2 or n = 0 (mod 4), and (b) for each prime divisor p of n, we have either (p/q) = 1 for each prime q 1 n2 -1 or for some positive integer r (which depends on p), n+lIp'+land