Steiner triple systems with block-transitive automorphism groups
نویسندگان
چکیده
منابع مشابه
Steiner Triple Systems with Doubly Transitive Automorphism Groups: A Corollary to the Classification Theorem for Finite Simple Groups
Assuming that the classification theorem for finite simple groups is complete, a conjecture of M. Hall (Proc. Sympos. Pure Math. 6 (1962), 47-66; and in “Proceedings of the International Conference on Theory of Groups,” pp. 115-144, Australian National University, Canberra, Australia, 1965) that a Steiner triple system with a doubly transitive automorphism group is a projective or afline geomet...
متن کاملAUTOMORPHISM GROUPS OF SOME NON-TRANSITIVE GRAPHS
An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for ij, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. Balaban introduced some monster graphs and then Randic computed complexit...
متن کاملSteiner Triple Systems of Order 19 with Nontrivial Automorphism Group
There are 172,248 Steiner triple systems of order 19 having a nontrivial automorphism group. Computational methods suitable for generating these designs are developed. The use of tactical configurations in conjunction with orderly algorithms underlies practical techniques for the generation of the designs, and the subexponential time isomorphism technique for triple systems is improved in pract...
متن کاملSteiner Quadruple Systems with Point-regular Abelian Automorphism Groups
Abstract. In this paper we present a graph theoretic construction of Steiner quadruple systems (SQS) admitting abelian groups as point-regular automorphism groups. The resulting SQS has an extra property which we call A-reversibility, where A is the underlying abelian group. In particular, when A is a 2-group of exponent at most 4, it is shown that an A-reversible SQS always exists. When the Sy...
متن کاملBlock transitive Steiner systems with more than one point orbit
For all ‘reasonable’ finite t, k and s we construct a t-(א0, k, 1) design and a group of automorphisms which is transitive on blocks and has s orbits on points. In particular, there is a 2-(א0, 4, 1) design with a block-transitive group of automorphisms having two point orbits. This answers a question of P. J. Cameron and C. E. Praeger. The construction is presented in a purely combinatorial wa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1976
ISSN: 0012-365X
DOI: 10.1016/0012-365x(76)90055-8