Cycle indices of PGL(2,q) acting on the cosets of its subgroups

Abstract

In this paper, we mainly investigate the action of 𝑃𝐺𝐿 2,𝑞 on the cosets some of its subgroups namely; 𝐶𝑞−1,𝐶𝑞+1and 𝑃 𝑞. Corresponding to each action the disjoint cycle structures and cycle index formulas is determined.