Finite Generalized Tetrahedron Groups with a High-Power Relator |
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Authors: | Martin Edjvet James Howie Gerhard Rosenberger Richard M. Thomas |
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Affiliation: | (1) School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, England;(2) Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, Scotland;(3) Fachbereich Mathematik, Universität Dortmund, 44221 Dortmund, Germany;(4) Department of Mathematics and Computer Science, University of Leicester, Leicester, LE1 7RH, England |
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Abstract: | An ordinary tetrahedron group is a group with a presentati on of the formwhere ei 2 and fi 2 for each i. Following Vinberg, we call groups defined by a presentation of the formwhere each Ri(a, b) is a cyclically reduced word involving both a and b, generalized tetrahedron groups. These groups appear in many contexts, not least as subgroups of generalized triangle groups.In this paper, we build on previous work to start on a complete classification as to which generalized tetrahedron groups are finite; here we treat the case where at least one of the fi is greater than three. |
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Keywords: | essential representation generalized tetrahedron group generalized triangle group spelling theorem trace polynomial triangle of groups |
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