Experimental Mathematics

Platonic triangles of groups

Roger C. Alperin

Full-text: Open access

Abstract

Non-positively curved triangles of finite groups are of cohomological dimension 2 over the rationals and have Property FA. We classify triangles of finite groups which satisfy certain geometric conditions including the Gauss--Bonnet theorem. We investigate whether or not these groups are virtually torsion-free, contain a free abelian subgroup of rank 2, are residually finite or are linear.

Article information

Source
Experiment. Math., Volume 7, Issue 3 (1998), 191-219.

Dates
First available in Project Euclid: 14 March 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1047674204

Mathematical Reviews number (MathSciNet)
MR1676687

Zentralblatt MATH identifier
0959.20039

Subjects
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15] 20F67: Hyperbolic groups and nonpositively curved groups

Keywords
Triangle of groups Coxeter group FA cohomological dimension

Citation

Alperin, Roger C. Platonic triangles of groups. Experiment. Math. 7 (1998), no. 3, 191--219. https://projecteuclid.org/euclid.em/1047674204


Export citation