Involve: A Journal of Mathematics

  • Involve
  • Volume 2, Number 3 (2009), 323-340.

The genus level of a group

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

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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.

Article information

Involve, Volume 2, Number 3 (2009), 323-340.

Received: 5 November 2008
Revised: 2 July 2009
Accepted: 6 July 2009
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H37: Automorphisms 30F20: Classification theory of Riemann surfaces

automorphism groups of compact Riemann surfaces hyperelliptic surfaces genus zero actions


Arbo, Matthew; Benkowski, Krystin; Coate, Ben; Nordstrom, Hans; Peterson, Chris; Wootton, Aaaron. The genus level of a group. Involve 2 (2009), no. 3, 323--340. doi:10.2140/involve.2009.2.323.

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