Geometric characterization of the sporadic groups Fi22, Fi23, and Fi24
Let Σ1, …, Σ4 be the 3-transposition graphs for Fischer's sporadic groups Fi21, …, Fi24. We classify connected locally Σi graphs gQ = gQi+1 for i = 1, 2, 3. In the minimal case i = 1 we also assume that for every nondegenerate 4-circuit abcd the subgraph Θ(a, b, c, d) is isomorphic to the disjo...
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| Format: | Article |
| Language: | English |
| Published: |
2013
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| Online Access: | https://hdl.handle.net/10356/87920 http://hdl.handle.net/10220/9439 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | Let Σ1, …, Σ4 be the 3-transposition graphs for Fischer's sporadic groups Fi21, …, Fi24. We classify connected locally Σi graphs gQ = gQi+1 for i = 1, 2, 3. In the minimal case i = 1 we also assume that for every nondegenerate 4-circuit abcd the subgraph Θ(a, b, c, d) is isomorphic to the disjoint union of three copies of K3,3. If i = 1, 2 then Θ is isomorphic to Σi+1, whereas if i = 3 then Θ is isomorphic either to Σ4 or to its 3-fold antipodal cover 3Σ4. |
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