Abstract
The problem of embedding the Witt-Mathieu system S(3, 6, 22) in a symmetric 2-(78, 22, 6) design is investigated. It is proved that the Mathieu group M 22, as well as its maximal subgroups M 21, 24 · A 6, PSL(2, 11) and 23 · PSL(3, 2) cannot be automorphism groups of an embedding. A symmetric design possessing the Witt-Mathieu system as a derived design and in variant under a maximal subgroup of 23 · PSL(3, 2) of order 168 is constructed. As a by-product, the existence of a quasi-symmetric 2-(56, 16, 6) design is established.
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Tonchev, V.D. Embedding of the Witt-Mathieu system S(3, 6, 22) in a symmetric 2-(78, 22, 6) design. Geom Dedicata 22, 49–75 (1987). https://doi.org/10.1007/BF00183053
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DOI: https://doi.org/10.1007/BF00183053