A characterization of 3-local geometry of M(24) |
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Authors: | A A Ivanov G Stroth |
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Institution: | (1) Department of Mathematics, Imperial College, 180 Queen's Gate, SW 2BZ London, UK;(2) Institut für Algebra und Geometrie, Fachbereich Mathematik u. Informatik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle, Germany |
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Abstract: | The largest Fischer 3-transposition group M(24) acts flag-transitively on a 3-local incidence geometry
(M(24)) which is a c-extension of the dual polar space associated with the group O
7(3). The action of the simple commutator subgroup M(24) is still flag-transitive. We show that
(M(24)) is characterized by its diagram under the flag-transitivity assumption. The result implies in particular that
(M(24)) is simply connected. The geometry
(M(24)) appears as a subgeometry in the Buekenhout-Fischer 3-local geometry
(F
1) of the Monster group. The simple connectedness of
(M(24)) has played a crucial role in the characterization of
(F
1), which has been achieved recently. When determining the possible structure of the parabolic subgroups we have used an unpublished pushing-up result by U. Meierfrankenfeld.Dedicated to Professor B. Fischer on the occasion of his sixtieth birthday |
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Keywords: | 51E24 20D08 |
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