Linear spaces with flag-transitive automophism groups

Buekenhout, Francis; Delandtsheer, Anne; Doyen, Jean; Kleidman, Peter P.B.; Liebeck, Martin W.; Saxl, Jan

doi:10.1007/bf00181466

Cited by 92 publications

(181 citation statements)

References 21 publications

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“…All the partial linear spaces in C 2 are flag-transitive, that is, the group G acts transitively on the set of point-line incident pairs. A classification of the subfamily consisting of the flag-transitive linear spaces, apart from the onedimensional affine case, was announced in [3] with proofs in [1,2,5,6,7,11,13,14].…”

Section: à ámentioning

confidence: 98%

Locally 2‐arc transitive graphs, homogeneous factorizations, and partial linear spaces

Giudici

Praeger

2005

J of Combinatorial Designs

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Section: à ámentioning

confidence: 98%

Locally 2‐arc transitive graphs, homogeneous factorizations, and partial linear spaces

Giudici

Praeger

2005

J of Combinatorial Designs

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“…(3, 3, 3) and (3, 3, 4): These two cases are flag-transitive linear spaces that we referred to earlier in the work of Higman and McLaughlin, and have been classified up to the one-dimensional affine case [11]. The parameters (3, 3, 3) yield projective planes, while the case (3, 3, 4) with point-order s p = 1 corresponds to complete graphs and 2-transitive group actions (which are known completely by the classification of the finite 2-transitive permutation groups).…”

Section: Coset Geometriesmentioning

confidence: 99%

Triple factorisations of the general linear group and their associated geometries

Alavi

Bamberg

Praeger

2015

Linear Algebra and its Applications

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Triple factorisations of finite groups G of the form G = P QP are essential in the study of Lie theory as well as in geometry. Geometrically, each triple factorisation G = P QP corresponds to a G-flag transitive point/line geometry such that 'each pair of points is incident with at least one line'. We call such a geometry collinearly complete, and duality (interchanging the roles of points and lines) gives rise to the notion of concurrently complete geometries. In this paper, we study triple factorisations of the general linear group GL(V ) as P QP where the subgroups P and Q either fix a subspace or fix a decomposition of V as V 1 ⊕ V 2 with dim(V 1 ) = dim(V 2 ).

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“…The work by Davies was subsumed in a more general classi®cation of linear spaces whose automorphism groups are¯ag-transitive which has been announced in [3]. A key step in this is the knowledge that if G is an automorphism group of a linear space S then G is primitive in the action on points (see [17]).…”

Section: Introductionmentioning

confidence: 99%