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The girth of convergence groups and mapping class groups. (English) Zbl 1270.20033
Summary: We give a sufficient condition for the girth of finitely generated groups to be infinite by using a technique to prove a so-called ping-pong lemma or table tennis lemma. We show that some convergence groups and subgroups of mapping class groups satisfy the condition. Therefore the girth of each of them is infinite.
MSC:
20F05 Generators, relations, and presentations of groups
20F38 Other groups related to topology or analysis
57M07 Topological methods in group theory
20F65 Geometric group theory
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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Full Text: Euclid
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