Generators of permutation groups simply isomorphic with 𝐿𝐹(2,𝑝ⁿ)

Abstract

It is well known that the group LF(2, p) of linear fractional transformations of determinant unity in the GF[p] can be represented as a permutation group G of degree p+l. The purpose of this note is to show that the generators of G follow from a slight extension of an argument used in a recent paper. We obtain a representation of the abstract group L simply isomorphic with the special linear homogeneous group SLH(2, p) by means of the cosets K and KTS\, where X ranges over the p marks of the field ^o( = 0), #1, • • • , um, (m = p n — \). Let ko0 = K and kUi = KTSUi for i = 0, 1, • • • , m. If p is any mark, KSP = K and KTS\SP = KTS\+P, so that to Sp there corresponds the permutation