Skip to main content
Surface Subgroups of Graph Groups
Proceedings of the American Mathematical Society
  • Herman J. Servatius, Worcester Polytechnic Institute
  • Carl Droms
  • Brigitte Servatius, Worcester Polytechnic Institute
Document Type
Publication Date
Given a graph F, define the group Fr to be that generated by the vertices of F, with a defining relation xy = yx for each pair x, y of adjacent vertices of F. In this article, we examine the groups Fr, where the graph F is an n-gon, (n > 4). We use a covering space argument to prove that in this case, the commutator subgroup F.' contains the fundamental group of the orientable surface of genus 1 + (n - 4)2n-3 . We then use this result to classify all finite graphs F for which Fr is a free group.
Publisher Statement

First published in Proceedings of the American Mathematical Society in 106(3), published by the American Mathematical Society.

Citation Information
Herman J. Servatius, Carl Droms and Brigitte Servatius. "Surface Subgroups of Graph Groups" Proceedings of the American Mathematical Society Vol. 106 Iss. 3 (1989) p. 573 - 578
Available at: