Quasifields with irreducible nuclei
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 exceptiona...
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117128400034X |
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| _version_ | 1832547455371051008 |
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| author | Michael J. Kallaher |
| author_facet | Michael J. Kallaher |
| author_sort | Michael J. Kallaher |
| collection | DOAJ |
| description | 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 52, 52, 72, or 112, 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. |
| format | Article |
| id | doaj-art-9cb5c66e9925462cbb93f9d04a402c0d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-9cb5c66e9925462cbb93f9d04a402c0d2025-02-03T06:44:46ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017231932610.1155/S016117128400034XQuasifields with irreducible nucleiMichael J. Kallaher0Department of Pure and Applied Mathematics, Washington State University, Pullman 99164-2930, Washington, USAThis 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 52, 52, 72, or 112, 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.http://dx.doi.org/10.1155/S016117128400034Xquasifieldstype L quasifieldsirreducibilitynucleus. |
| spellingShingle | Michael J. Kallaher Quasifields with irreducible nuclei International Journal of Mathematics and Mathematical Sciences quasifields type L quasifields irreducibility nucleus. |
| title | Quasifields with irreducible nuclei |
| title_full | Quasifields with irreducible nuclei |
| title_fullStr | Quasifields with irreducible nuclei |
| title_full_unstemmed | Quasifields with irreducible nuclei |
| title_short | Quasifields with irreducible nuclei |
| title_sort | quasifields with irreducible nuclei |
| topic | quasifields type L quasifields irreducibility nucleus. |
| url | http://dx.doi.org/10.1155/S016117128400034X |
| work_keys_str_mv | AT michaeljkallaher quasifieldswithirreduciblenuclei |