Quasifields with irreducible nuclei
1984 ◽
Vol 7
(2)
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pp. 319-326
This article considers finite quasifields having a subgroupNof either the right or middle nucleus ofQwhich acts irreducibly as a group of linear transformations onQas a vector space over its kernel. It is shown thatQis a generalized André system, an irregular nearfield, a Lüneburg exceptional quasifield of typeR∗por typeF∗p, or one of four other possibilities having order52,52,72, or112, 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.
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1998 ◽
Vol 57
(1)
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pp. 59-71
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1975 ◽
Vol 27
(3)
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pp. 561-572
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1976 ◽
Vol 28
(3)
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pp. 455-472
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2017 ◽
Vol 103
(3)
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pp. 402-419
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1975 ◽
Vol 27
(3)
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pp. 666-678
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1957 ◽
Vol 11
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pp. 125-130
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