Vol. 2, No. 3, 2009

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ISSN: 1944-4184 (e-only)
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The genus level of a group

Matthew Arbo, Krystin Benkowski, Ben Coate, Hans Nordstrom, Chris Peterson and Aaron Wootton

Vol. 2 (2009), No. 3, 323–340
Abstract

We introduce the notion of the genus level of a group as a tool to help classify finite conformal group actions on compact Riemann surfaces. We classify all groups of genus level 1 and use our results to outline an algorithm to classify actions of p-groups on compact Riemann surfaces. To illustrate our results, we provide a number of detailed examples.

Keywords
automorphism groups of compact Riemann surfaces, hyperelliptic surfaces, genus zero actions
Mathematical Subject Classification 2000
Primary: 14H37, 30F20
Milestones
Received: 5 November 2008
Revised: 2 July 2009
Accepted: 6 July 2009
Published: 3 October 2009

Communicated by Nigel Boston
Authors
Matthew Arbo
University of Oregon
Department of Mathematics
Fenton Hall, 1222
Eugene, OR 97403
United States
http://uoregon.edu/~arbo
Krystin Benkowski
Western Michigan University
Department of Mathematics
3319 Everett Tower
Kalamazoo, MI 49008
United States
Ben Coate
Rensselaer Polytechnic Institute
School of Architecture
Greene Building
110 8th street
Troy, NY 12180
United States
Hans Nordstrom
University of Portland
Department of Mathematics
5000 North Willamette Blvd.
Portland, OR 97203
United States
http://faculty.up.edu/nordstro/
Chris Peterson
Pomona College
Department of Mathematics
610 North College Avenue
Claremont, CA 91711
United States
Aaron Wootton
University of Portland
Department of Mathematics
5000 North Willamette Blvd.
Portland, OR 97203
United States
http://faculty.up.edu/wootton/