Translation planes of even order in which the dimension has only one odd factor

T. G. Ostrom

International Journal of Mathematics and Mathematical Sciences, 1980, vol. 3, 1-20

Abstract:

Let G be an irreducible subgroup of the linear translation complement of a finite translation plane of order q d where q is a power of 2 . G F ( q ) is in the kernel and d = 2 s r where r is an odd prime. A prime factor of | G | must divide ( q d + 1 ) ∏ i = 1 d ( q i − 1 ) .

One possibility (there are no known examples) is that G has a normal subgroup W which is a W -group for some prime W .

The maximal normal subgroup 0 ( G ) satisfies one of the following:

1. Cyclic. 2. Normal cyclic subgroup of index r and the nonfixed-point-free elements in 0 ( G ) have order r . 3. 0 ( G ) contains a group W as above.

Date: 1980
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:343279

DOI: 10.1155/S0161171280000488

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