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2017•Transactions of A Razmadze Mathematical InstituteOpen access

Actions of Δ(3,n,k) on projective line

Muhammad Naeem Ashiq, Tahir Imran, Muhammad Asad Zaighum

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Abstract

Each conjugacy class of actions of the triangle group Δ(3,n,k) over the projective line PL(Fq) can be represented by a coset diagram D(θ,q), where θ∈Fq and q is a prime number. In this paper, we have considered conjugacy classes which arise from the actions of Δ(3,n,k)=〈r,s:r3=sn=(rs)k=1〉 over PL(Fq), where Fq is finite field. The points of PL(Fq) are the elements of Fq together with the additional point ∞.

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What this paper is about

Each conjugacy class of actions of the triangle group Δ(3,n,k) over the projective line PL(Fq) can be represented by a coset diagram D(θ,q), where θ∈Fq and q is a prime number. In this paper, we have considered conjugacy classes which arise from the actions of Δ(3,n,k)=〈r,s:r3=sn=(rs)k=1〉 over PL(Fq), where Fq is finite field. The points of PL(Fq) are the elements of Fq together with the additional point ∞.

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Available abstract

Each conjugacy class of actions of the triangle group Δ(3,n,k) over the projective line PL(Fq) can be represented by a coset diagram D(θ,q), where θ∈Fq and q is a prime number. In this paper, we have considered conjugacy classes which arise from the actions of Δ(3,n,k)=〈r,s:r3=sn=(rs)k=1〉 over PL(Fq), where Fq is finite field. The points of PL(Fq) are the elements of Fq together with the additional point ∞.

Key concepts: Conjugacy class, Combinatorics, Mathematics, Line (geometry), Prime (order theory), Discrete mathematics, Algorithm, Geometry

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