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A design and a geometry for the group Fi\(_{22}\). (English) Zbl 1127.05008

Summary: The Fischer group Fi\(_{22}\) acts as a rank 3 group of automorphisms of a symmetric 2-\((14080,1444,148)\) design. This design does not have a doubly transitive automorphism group, since there is a partial linear space with lines of size 4 defined combinatorially from the design and preserved by its automorphism group. We investigate this geometry and determine the structure of various subspaces of it.

MSC:

05B05 Combinatorial aspects of block designs
05B25 Combinatorial aspects of finite geometries
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
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