Finite line-transitive linear spaces: Theory and search strategies
نویسندگان
چکیده
منابع مشابه
Finite 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...
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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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The paper studies line-transitive, point-imprimitive automorphism groups G of finite linear spaces. In particular, it explores inequalities involving two integer parameters x; y introduced by Delandtsheer and Doyen associated with a given G-invariant partition C of the point set. There is special interest in the case where C is G-normal, that is, C is the set of orbits of a normal subgroup of G...
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ژورنال
عنوان ژورنال: Acta Mathematica Sinica, English Series
سال: 2009
ISSN: 1439-8516,1439-7617
DOI: 10.1007/s10114-009-9275-0