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- Title
Deformation theory and finite simple quotients of triangle groups I.
- Authors
Larsen, Michael; Lubotzky, Alexander; Marion, Claude
- Abstract
Let 2 ≤ a ≤ b ≤ c ∈ N with μ = 1/a + 1/b + 1/c < 1 and let T + Ta,b,c = (x, y, z: xa = yb = zc = xyz = 1) be the corresponding hyperbolic triangle group. Many papers have been dedicated to the following question: what are the finite (simple) groups which appear as quotients of T = (Classically, for (a, b, c) = (2, 3, 7) and more recently also for general (a, b, c).) These papers have used either explicit constructive methods or probabilistic ones. The goal of this paper is to present a new approach based on the theory of representation varieties (via deformation theory). As a corollary we essentially prove a conjecture of Marion [21] showing that various finite simple groups are not quotients of T, as well as positive results showing that many finite simple groups are quotients of T.
- Subjects
FINITE simple groups; HYPERBOLIC groups; VARIETIES (Universal algebra); QUOTIENT rings; PROBABILITY theory
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2014, Vol 16, Issue 7, p1349
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/463