Quasifields with irreducible nuclei

Michael J. Kallaher

International Journal of Mathematics and Mathematical Sciences, 1984, vol. 7, 1-8

Abstract:

This article considers finite quasifields having a subgroup N of either the right or middle nucleus of Q which acts irreducibly as a group of linear transformations on Q as a vector space over its kernel. It is shown that Q is a generalized André system, an irregular nearfield, a Lüneburg exceptional quasifield of type R ∗ p or type F ∗ p , or one of four other possibilities having order 5 2 , 5 2 , 7 2 , or 11 2 , respectively. This result generalizes earlier work of Lüneburg and Ostrom characterizing generalized André systems, and it demonstrates the close similarity of the Lüneburg exceptional quasifields to the generalized André system.

Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:940202

DOI: 10.1155/S016117128400034X

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