JOINING OF CIRCUITS IN PSL(2, ℤ)-SPACE

Title & Authors
JOINING OF CIRCUITS IN PSL(2, ℤ)-SPACE
MUSHTAQ, QAISER; RAZAQ, ABDUL;

Abstract
The coset diagrams are composed of fragments, and the fragments are further composed of circuits at a certain common point. A condition for the existence of a certain fragment $\small{{\gamma}}$ of a coset diagram in a coset diagram is a polynomial f in $\small{{\mathbb{Z}}}$[z]. In this paper, we answer the question: how many polynomials are obtained from the fragments, evolved by joining the circuits (n, n) and (m, m), where n < m, at all points.
Keywords
modular group;coset diagrams;projective line over finite field;
Language
English
Cited by
References
1.
M. Akbas, On suborbital graphs for the modular group, Bull. Lond. Math. Soc. 33 (2001), no. 6, 647-652.

2.
B. Everitt, Alternating quotients of the (3, q, r) triangle groups, Comm. Algebra 25 (1997), no. 6, 1817-1832.

3.
E. Fujikawa, Modular groups acting on in nite dimensional Teichmuller spaces, In the tradition of Ahlfors and Bers, III, 239-253, Contemp. Math., 355, Amer. Math. Soc., Providence, RI, 2004.

4.
G. Higman and Q. Mushtaq, Generators and relations for PSL(2, $\mathbb{Z}$), Gulf J. Sci. Res. 31 (1983), no. 1, 159-164.

5.
O. Koruoglu, The determination of parabolic points in modular and extended modular groups by continued fractions, Bull. Malays. Math. Sci. Soc. (2) 33 (2010), no. 3, 439-445.

6.
Q. Mushtaq, A condition for the existence of a fragment of a coset diagram, Quart. J. Math. Oxford Ser. (2) 39 (1988), no. 153, 81-95.

7.
Q. Mushtaq, Parameterization of all homomorphisms from PGL(2, $\mathbb{Z}$) into PSL(2, q), Comm. Algebra 4 (1992), no. 20, 1023-1040.

8.
Q. Mushtaq and G.-C. Rota, Alternating groups as quotients of two generator group, Adv. Math. 96 (1993), no. 1, 113-1211.

9.
Q. Mushtaq and H. Servatius, Permutation representation of the symmetry groups of regular hyperbolic tessellations, J. London Math. Soc. (2) 48 (1993), no. 1, 77-86.

10.
Q. Mushtaq and A. Razaq, Equivalent pairs of words and points of connection, Sci. World J. 2014 (2014), Article ID 505496, 8 pages.

11.
A. Torstensson, Coset diagrams in the study of nitely presented groups with an appli- cation to quotients of the modular group, J. Commut. Algebra 2 (2010), no. 4, 501-514.