Name
Abstract | ||
|---|---|---|
The symmetric genus of the finite group G, denoted by sigma(G), is the smallest nonnegative integer g such that the group G acts faithfully on a closed orientable surface of genus g (not necessarily preserving orientation). This paper investigates the question of whether for every non-negative integer g, there exists some G with symmetric genus g. It is shown that that the spectrum (range of values) of sigma includes every non-negative integer g 8 or 14 mod 18, and moreover, if a gap occurs at some g equivalent to 8 or 14 modulo 18, then the prime-power factorization of g - 1 includes some factor p(e) equivalent to 5 mod 6. In fact, evidence suggests that this spectrum has no gaps at all. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.26493/1855-3974.127.eb9 | ARS MATHEMATICA CONTEMPORANEA |
Keywords | Field | DocType |
Symmetric genus,Riemann surface,Riemann-Hurwitz equation,NEC group,signature | Integer,Discrete mathematics,Combinatorics,Existential quantification,Modulo,Factorization,Finite group,Mathematics | Journal |
Volume | Issue | ISSN |
4 | SP2 | 1855-3966 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marston D. E. Conder | 1 | 233 | 34.35 |
| Thomas W. Tucker | 2 | 191 | 130.07 |