THIS paper concerns maximal subgroups of symmetric groups on infinite, usually countable, sets. Our main aim is to give examples of maximal subgroups which could claim to be almost stabilisers of familiar combinatorial structures. We emphasise that maximal subgroup always means maximal proper subgroup. Throughout this paper, Cl will denote an infinite set, usually countable. The power set of Q ...

For a maximal subgroup M of a finite group G , the normal index r¡(G : M) is defined to be the order of a chief factor H/K where H is minimal in the set of supplements of M in G . We obtain several results on the normal index of maximal subgroups M of composite index in G with [G : M]p = 1 which imply G to be solvable, supersolvable.