Singer Groups

Source abstract

Interest in the Singer groups has arisen in various places. The name itself results from the connection Singer [ 7 ] made between these groups and perfect difference sets, and this is closely associated with the geometric property that a Singer group is regular on the points of a projective space. Some information about these groups appears in Huppert's book [ 3 , p. 187]. Singer groups are frequently useful in constructing examples and counterexamples. Our aim in this paper is to make a systematic study of the Singer subgroups of the linear groups, with a particular view to analyzing the examples they provide of Frobenius regular groups. Frobenius regular groups are a class of permutation groups generalizing the Zassenhaus groups, and Keller [ 5 ] has shown recently that they provide a new characterization of A 6 and M 11 .