April 2024 MAXIMAL ORDER GROUP ACTIONS ON RIEMANN SURFACES OF GENUS 1+3p
Coy L. May, Jay Zimmerman
Rocky Mountain J. Math. 54(2): 495-508 (April 2024). DOI: 10.1216/rmj.2024.54.495

Abstract

A natural problem is to determine, for each value of the integer g2, the largest order of a group that acts on a Riemann surface of genus g. Let N(g) (respectively M(g)) be the largest order of a group of automorphisms of a Riemann surface of genus g2 preserving the orientation (respectively possibly reversing the orientation) of the surface.

Let g=1+3p for a large prime p. It has been established that if p is congruent to 1(mod6), then N(g)=M(g)=24(g1). Suppose p is congruent to 5(mod6). We prove that if p is also congruent modulo 25 to 1, 6, 11 or 16, then N(g)=8(g+11) and M(g)=16(g+11); otherwise N(g)=8(g+1) and M(g)=16(g+1).

Citation

Download Citation

Coy L. May. Jay Zimmerman. "MAXIMAL ORDER GROUP ACTIONS ON RIEMANN SURFACES OF GENUS 1+3p." Rocky Mountain J. Math. 54 (2) 495 - 508, April 2024. https://doi.org/10.1216/rmj.2024.54.495

Information

Received: 15 June 2022; Revised: 3 February 2023; Accepted: 3 February 2023; Published: April 2024
First available in Project Euclid: 7 May 2024

Digital Object Identifier: 10.1216/rmj.2024.54.495

Subjects:
Primary: 57M60
Secondary: 20F38 , 20H10

Keywords: genus , group action , NEC group , Riemann surface

Rights: Copyright © 2024 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
14 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

Vol.54 • No. 2 • April 2024
Back to Top