## Abstract

A locally projective amalgam is formed by the stabilizer G(x) of a vertex x and the global stabilizer G{x, y} of an edge (containing x) in a group G, acting faithfully and locally finitely on a connected graph γ of valency 2^{n}-1 so that (i) the action is 2-arc-transitive; (ii) the subconstituent G(x)^{γ(x)} is the linear group SL_{n}(2) ≅ L_{n}(2) in its natural doubly transitive action and (iii) {t, G{x, y}] ≤ O_{2}(G(x) γ G{x, y}) for some t ε G{x, y} \ G(x). D. Ž. Djoković and G. L. Miller [DM80], used the classical Tutte's theorem [Tu47], to show that there are seven locally projective amalgams for n = 2. Here we use the most difficult and interesting case of Trofimov's theorem [Tr01] to extend the classification to the case n ≥ 3. We show that besides two infinite series of locally projective amalgams (embedded into the groups AGL_{n}(2) and O_{2n}^{+}(2)) there are exactly twelve exceptional ones. Some of the exceptional amalgams are embedded into sporadic simple groups M_{22}, M_{23}, Co_{2}, J _{4} and BM. For each of the exceptional amalgam n = 3, 4 or 5.

Original language | English |
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Pages (from-to) | 19-98 |

Number of pages | 80 |

Journal | Nagoya Mathematical Journal |

Volume | 176 |

DOIs | |

Publication status | Published - Dec 2004 |

## ASJC Scopus subject areas

- General Mathematics