The Residually Weakly Primitive Geometries of M22
نویسنده
چکیده
In [6], Dehon and the author described two algorithms to classify all geometries Γ of a given group G such that Γ is a firm and residually connected geometry and G acts flag-transitively and residually weakly primitively on Γ. We stated in that paper that these programs were able to classify all geometries with Borel subgroup not equal to the identity of G when G is the Hall-Janko group J2. In the meantime, we have succeeded in classifying all geometries with Borel subgroup the identity of G for J2 as we describe in Section 2. In the present paper, we announce the results we obtained using our set of programs. These programs were written in Magma [1]. The paper is organised as follows. In section 1, we recall the basic definitions needed to understand this paper. In section 2, we explain how we dealt with the case where the Borel subgroup is reduced to the identity for the Hall-Janko group J2. In section 3, we state the results obtained and state some facts concerning these results. Finally, in section 4, we describe what can be found in the supplement to this paper [9].
منابع مشابه
Rank Three Residually Connected Geometries for M22, Revisited
The rank 3 residually connected flag transitive geometries Γ for M22 for which the stabilizer of each object in Γ is a maximal subgroup of M22 are determined. As a result this deals with the infelicities in Theorem 3 of Kilic and Rowley, On rank 2 and rank 3 residually connected geometries for M22. Note di Matematica, 22(2003), 107–154.
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ورودعنوان ژورنال:
- Des. Codes Cryptography
دوره 29 شماره
صفحات -
تاریخ انتشار 2003