论文信息 - REGULAR HYPERMAPS OVER PROJECTIVE LINEAR GROUPS

REGULAR HYPERMAPS OVER PROJECTIVE LINEAR GROUPS

Abstract An enumeration result for orientably regular hypermaps of a given type with automorphism groups isomorphic to PSL(2,q) or PGL(2,q) can be extracted from a 1969 paper by Sah. We extend the investigation to orientable reflexible hypermaps and to nonorientable regular hypermaps, providing many more details about the associated computations and explicit generating sets for the associated groups.

[1] Gareth Jones,et al. Suzuki Groups and Surfaces , 1993 .

[2] A. M. Macbeath,et al. Generators of the linear fractional groups , 1969 .

[3] G. Jones,et al. Belyi Functions, Hypermaps and Galois Groups , 1996 .

[4] Jozef Širáň,et al. Regular maps with almost Sylow-cyclic automorphism groups, and classification of regular maps with Euler characteristic −p 2 , 2010 .

[5] G. Rosenberger,et al. Erzeugende endlicher projektiver linearer Gruppen , 1989 .

[6] Leila Schneps,et al. The Grothendieck theory of dessins d'enfants , 1994 .

[7] David Singerman,et al. The Grothendieck theory of dessins d'enfants: Maps, Hypermaps and Triangle Groups , 1994 .

[8] C. Sah. Groups related to compact Riemann surfaces , 1969 .

[9] G. Jones,et al. Platonic Hypermaps , 2000 .

[10] Regular maps with automorphism group PSL2{q) , 1997 .

[11] G. Rosenberger,et al. Generators of finite protective linear groups: Part 2 , 1990 .

[12] G. A. Jones,et al. Ree Groups and Riemann Surfaces , 1994 .

[13] L. Dickson. Linear Groups, with an Exposition of the Galois Field Theory , 1958 .