Line-transitive point-imprimitive linear spaces: the grid case
نویسندگان
چکیده
منابع مشابه
Classification of line-transitive point-imprimitive linear spaces with line size at most 12
In this paper we complete a classification of finite linear spaces S with line size at most 12 admitting a line-transitive point-imprimitive subgroup of automorphisms. The examples are the Desarguesian projective planes of orders 4, 7, 9 and 11, two designs on 91 points with line size 6, and 467 designs on 729 points with line size 8.
متن کاملA pr 2 00 6 Searching for Line Transitive , Point Imprimitive , Linear Spaces 1
A finite linear space is a finite set of points and lines, where any two points lie on a unique line. Well known examples include projective planes. This project focuses on linear spaces which admit certain types of symmetries. Symmetries of the space which preserve the line structure are called automorphisms. A group of these is called an automorphism group of the linear space. Two interesting...
متن کامل2 00 7 Classification of line - transitive point - imprimitive linear spaces with line size at most 12 Cheryl
In this paper we complete a classification of finite linear spaces S with line size at most 12 admitting a line-transitive point-imprimitive subgroup of automorphisms. The examples are the Desarguesian projective planes of orders 4, 7, 9 and 11, two designs on 91 points with line size 6, and 467 designs on 729 points with line size 8.
متن کاملFinite line-transitive linear spaces: parameters and normal point-partitions
Until the 1990’s the only known finite linear spaces admitting line-transitive, pointimprimitive groups of automorphisms were Desarguesian projective planes and two linear spaces with 91 points and line size 6. In 1992 a new family of 467 such spaces was constructed, all having 729 points and line size 8. These were shown to be the only linear spaces attaining an upper bound of Delandtsheer and...
متن کاملLine-transitive Automorphism Groups of Linear Spaces
In this paper we prove the following theorem. Let S be a linear space. Assume that S has an automorphism group G which is line-transitive and point-imprimitive with k < 9. Then S is one of the following:(a) A projective plane of order 4 or 7, (a) One of 2 linear spaces with v = 91 and k = 6, (b) One of 467 linear spaces with v = 729 and k = 8. In all cases the full automorphism group Aut(S) is ...
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ژورنال
عنوان ژورنال: Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial
سال: 2008
ISSN: 2640-7345,2640-7337
DOI: 10.2140/iig.2008.8.117