International Congress of Mathematicians

Permutation Groups and Normal Subgroups 69in £ if K,H £ £, H < K, and there are no intermediate subgroups lying in £.The basic components of G relative to £ are then defined as all the componentsComp(F', H) for which K covers H in £. Each maximal chain G Q = Go < Gi 2).A finite graph F = (Q, E) consists of a finite set 0 of points, called vertices, anda subset E of unordered pairs from Q called edges. For s > 1, an s-arc of F is a vertexsequence (ao,ai,... ,a s ) such that each {ai,ai + i} is an edge and a,_i ^ a, + i forall i. We usually call a 1-arc simply an arc. Automorphisms of F are permutationsof 0 that leave E invariant, and a subgroup G of the automorphism group Aut(F) is