Mathematics – Combinatorics
Scientific paper
2007-01-23
Acta Mathematica Sinica, English Series. 25 (2009), 1399-1436
Mathematics
Combinatorics
47 pages Version 1 had bbl file omitted. Apologies
Scientific paper
10.1007/s10114-009-9275-0
In 1991, Weidong Fang and Huiling Li proved that there are only finitely many non-trivial linear spaces that admit a line-transitive, point-imprimitive group action, for a given value of gcd(k,r), where k is the line size and r is the number of lines on a point. The aim of this paper is to make that result effective. We obtain a classification of all linear spaces with this property having gcd(k,r) at most 8. To achieve this we collect together existing theory, and prove additional theoretical restrictions of both a combinatorial and group theoretic nature. These are organised into a series of algorithms that, for gcd(k,r) up to a given maximum value, return a list of candidate parameter values and candidate groups. We examine in detail each of the possibilities returned by these algorithms for gcd(k,r) at most 8, and complete the classification in this case.
Betten Anton
Delandtsheer Anne
Law Maska
Niemeyer Alice C.
Praeger Cheryl E.
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