c-Extensions of the Petersen Geometry for M22

  title={c-Extensions of the Petersen Geometry for M22},
  author={Anna Fukshansky and Corinna Wiedorn},
  journal={Eur. J. Comb.},
In this paper we consider a group G acting flag-transitively on a geometry with diagram ◦ ◦ ◦ ◦ c P∗ 1 2 3 4 such that the residue of an element of type 1 is the Petersen geometry for the group M22. Explicitly, G is generated by finite subgroups P1, P2, P3, P4 such that (a) G 6= Gi := 〈Pj | j 6= i 〉 for 1≤ i ≤ 4. (b) For B := P1 ∩ P2 ∩ P3 ∩ P4 we haveBG = 1, whereBG :=⋂g∈G Bg. (c) If Ki = BGi , Gi j = 〈Pk|k 6= i, j 〉 andKi j = BGi j , thenG1/K1 ∼= M22 or Aut(M22) and the structures of the Gi… CONTINUE READING

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