Cycle indices of PGL(2,q) acting on the cosets of its subgroups
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International Journal of Scientific Research and Innovative Technology
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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.