Premium
Affine Distance‐Transitive Graphs and Exceptional Chevalley Groups
Author(s) -
Bon John Van,
Cohen Arjeh M.
Publication year - 2001
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/83.1.51
Subject(s) - mathematics , semidirect product , combinatorics , vector space , graph , group of lie type , affine transformation , transitive relation , primitive permutation group , discrete mathematics , group (periodic table) , pure mathematics , symmetric group , group theory , chemistry , organic chemistry , cyclic permutation
Suppose r = p b , where p is a prime. Let V be an n ‐dimensional GF( r )‐space and G a subgroup of AΓL( V ) ≅ AΓL( n , r ) containing all translations and acting primitively on the set of vectors in V . Denote by G 0 the stabilizer in G of the zero vector, so that G 0 ⩽ Γ L( V ) ≅ Γ L( n , r ) and G is the semidirect product of V and G 0 . Suppose that the generalized Fitting subgroup F *( G 0 ) of G 0 is an exceptional (twisted or untwisted, quasisimple) Chevalley group and that Γ is a graph structure on V on which G acts primitively and distance transitively. The content of this paper is that then G and Γ are known. This result solves an open case in the outstanding problem of classifying all finite primitive distance‐transitive groups. 2000 Mathematics Subject Classification : primary 20B25; secondary 05C25, 20Gxx, 05E30.