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- Alan R. Camina, Johannes Siemons
- J. Comb. Theory, Ser. A
- 1989

A 2-(u, k, 1) block design is a set Q of v points and a collection of k-subsets of 9, called blocks, such that any two points lie in a unique block. Such designs have been classified in [ l&S] if their automorphism group acts doubly transitively or doubly homogeneously on its points. A classification for the case of flag transitive automorphism groups is… (More)

- Alan R. Camina, Susanne Mischke
- Electr. J. Comb.
- 1996

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… (More)

- Alan R. Camina
- Discrete Mathematics
- 1985

- A. R. Camina
- 2011

* Supported by a grant from the Graduiertenkolleg " Analyse und Konstruktion in der Mathematik " , RWTH Aachen.

- ALAN R. CAMINA
- 2006

This note is part of a general programme to classify the automorphism groups of finite linear spaces. There have been a number of contributions to this programme, including two recent surveys [8, 3]. One of the most significant contributions was the classification of flag-transitive linear spaces [2]. Since then, the effort has been to classify the… (More)

A proper non-empty subset C of the points of a linear space S = (P; L) is called line-closed if any two intersecting lines of S , each meeting C at least twice, have their intersection in C. We show that when every line has k points and every point lies on r lines the maximum size for such sets is r + k ? 2. In addition it is shown that this cannot happen… (More)

- Alan R. Camina
- 1995

This note is part of a general programme to classify the automorphism groups of nite linear spaces. There have been a number of contributions to this programme including two recent surveys, 8, 3]. One of the most signiicant contributions was the classiication of ag-transitive linear spaces, 1]. Since then the eeort has been to classify the line-transitive… (More)

Suppose that a group G has socle L a simple large-rank classical group. Suppose furthermore that G acts transitively on the set of lines of a linear space S. We prove that, provided L has dimension at least 25, then G acts transitively on the set of flags of S and hence the action is known. For particular families of classical groups our results hold for… (More)

- A. R. CAMINA
- 2006

Let D:= (X,B,I) be a 2-design. For each xeX set Bx:= {jeB:xIj}, and define Xh dually for each h e B. We call D reduced if Xh = Xt implies that h = i for all h,ieB. Assume that D is a reduced 2-design with parameters v, b, k, r, X. Let G be a flag transitive automorphism group of D. By F*(G) we mean (as usual) the generalized Fitting subgroup of G which is… (More)

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