Collineation groups of translation planes of small dimension
A subgroup of the linear translation complement of a translation plane is geometrically irreducible if it has no invariant lines or subplanes. A similar definition can be given for geometrically primitive. If a group is geometrically primitive and solvable then it is fixed point free or metacyclic o...
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| Format: | Article |
| Language: | English |
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Wiley
1981-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171281000549 |
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| _version_ | 1850162006227681280 |
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| author | T. G. Ostrom |
| author_facet | T. G. Ostrom |
| author_sort | T. G. Ostrom |
| collection | DOAJ |
| description | A subgroup of the linear translation complement of a translation plane is
geometrically irreducible if it has no invariant lines or subplanes. A similar definition can be given for geometrically primitive. If a group is geometrically primitive and solvable then it is fixed point free or metacyclic or has a normal subgroup of order w2a+b where wa divides the dimension of the vector space. Similar conditions hold for solvable normal subgroups of geometrically primitive nonsolvable groups. When the dimension of the vector space is small there are restrictions on the group which might possibly be in the translation complement. We look at the situation for certain orders of the plane. |
| format | Article |
| id | doaj-art-fd4d618e915446cda0b60c1928f507f1 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1981-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-fd4d618e915446cda0b60c1928f507f12025-08-20T02:22:40ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251981-01-014471172410.1155/S0161171281000549Collineation groups of translation planes of small dimensionT. G. Ostrom0Department of Pure and Applied Mathematics, Washington State University, Pullman 99164, Washington, USAA subgroup of the linear translation complement of a translation plane is geometrically irreducible if it has no invariant lines or subplanes. A similar definition can be given for geometrically primitive. If a group is geometrically primitive and solvable then it is fixed point free or metacyclic or has a normal subgroup of order w2a+b where wa divides the dimension of the vector space. Similar conditions hold for solvable normal subgroups of geometrically primitive nonsolvable groups. When the dimension of the vector space is small there are restrictions on the group which might possibly be in the translation complement. We look at the situation for certain orders of the plane.http://dx.doi.org/10.1155/S0161171281000549translation planestranslation complementlinear groups. |
| spellingShingle | T. G. Ostrom Collineation groups of translation planes of small dimension International Journal of Mathematics and Mathematical Sciences translation planes translation complement linear groups. |
| title | Collineation groups of translation planes of small dimension |
| title_full | Collineation groups of translation planes of small dimension |
| title_fullStr | Collineation groups of translation planes of small dimension |
| title_full_unstemmed | Collineation groups of translation planes of small dimension |
| title_short | Collineation groups of translation planes of small dimension |
| title_sort | collineation groups of translation planes of small dimension |
| topic | translation planes translation complement linear groups. |
| url | http://dx.doi.org/10.1155/S0161171281000549 |
| work_keys_str_mv | AT tgostrom collineationgroupsoftranslationplanesofsmalldimension |