The conjugacy problem for Coxeter groups

We prove that for every finite rank Coxeter group there exists a polynomial (cubic) solution to the conjugacy problem.

[1]  P. Caprace.  Conjugacy of 2-spherical subgroups of Coxeter groups and parallel walls , 2005, math/0508057.

[2]  K. Strambach,et al.  Generators and Relations in Groups and Geometries , 1991 .

[3]  R. Howlett.  Normalizers of Parabolic Subgroups of Reflection Groups , 1980 .

[4]  David B. A. Epstein,et al.  Word processing in groups , 1992 .

[5]  L. E. Dickson.  Group Theory: 8 , 1905 .

[6]  Yu. I. Manin,et al.  Course in mathematical logic , 1977, Graduate texts in mathematics.

[7]  On Geometric Flats in the CAT(0) Realization of Coxeter Groups and Tits Buildings , 2006, Canadian Journal of Mathematics.

[8]  H. S. M. Coxeter,et al.  The Complete Enumeration of Finite Groups of the Form Ri2=(RiRj)kij=1 , 1935 .

[9]  Michael Davis,et al.  The geometry and topology of Coxeter groups , 2008 .

[10]  J. Humphreys.  Reflection groups and coxeter groups , 1990 .

[11]  G. E. Collins,et al.  Real Zeros of Polynomials , 1983 .

[12]  R. Howlett,et al.  A finiteness property an an automatic structure for Coxeter groups , 1993 .

[13]  Bruno Buchberger,et al.  Computer algebra symbolic and algebraic computation , 1982, SIGS.

[14]  È. Vinberg,et al.  Hyperbolic reflection groups , 1985 .

[15]  John Milnor,et al.  A note on curvature and fundamental group , 1968 .

[16]  B. Rémy,et al.  Simplicity and superrigidity of twin building lattices , 2006, math/0607664.

[17]  N. Jacobson.  Lectures In Abstract Algebra , 1951 .

[18]  Bernhard Mühlherr,et al.  Reflection triangles in Coxeter groups and biautomaticity , 2005 .

[19]  B. Rémy,et al.  Flat rank of automorphism groups of buildings , 2005, math/0510290.

[20]  R. Benedetti,et al.  Lectures on Hyperbolic Geometry , 1992 .

[21]  M. Dehn.  Über unendliche diskontinuierliche Gruppen , 1911 .

[22]  A. Beardon.  The Geometry of Discrete Groups , 1995 .

[23]  R. Dye.  GEOMETRY OF COXETER GROUPS (Research Notes in Mathematics, 54) , 1983 .

[24]  P. Caprace.  Conjugacy of one-ended subgroups of Coxeter groups and parallel walls , 2005 .

[25]  Louis Solomon,et al.  A Mackey formula in the group ring of a Coxeter group , 1976 .

[26]  Matthew Dyer,et al.  Reflection subgroups of Coxeter systems , 1990 .

[27]  A. Brøndsted.  An Introduction to Convex Polytopes , 1982 .

[28]  Jacques Tits,et al.  Le problème des mots dans les groupes de Coxeter , 1969 .

[29]  George Maxwell,et al.  Sphere packings and hyperbolic reflection groups , 1982 .

[30]  Buildings with isolated subspaces and relatively hyperbolic Coxeter groups , 2007, math/0703799.

[31]  M. Bridson,et al.  Metric Spaces of Non-Positive Curvature , 1999 .

[32]  A. Cohen.  Coxeter groups and three related topics , 1991 .

[33]  N. Jacobson,et al.  Lectures in Abstract Algebra : vol. III, Theory of Fields and Galois Theory. By N. Jacobson. Pp. xi, 323. 76s. (Van Nostrand) , 1966, The Mathematical Gazette.

[34]  Luis Paris.  Irreducible Coxeter Groups , 2007, Int. J. Algebra Comput..

[35]  Arjeh M. Cohen.  Recent results on Coxeter groups , 1994 .

[36]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[37]  Vinay V. Deodhar.  On the root system of a coxeter group , 1982 .

[38]  Athanase Papadopoulos,et al.  Géométrie et théorie des groupes , 1990 .

[39]  H. Short,et al.  Notes on word hyperbolic groups , 1991 .

[40]  Udo Baumgartner,et al.  Totally Disconnected, Locally Compact Groups as Geometric Objects , 2007 .

[41]  Vinay V. Deodhar.  A note on subgroups generated by reflections in Coxeter groups , 1989 .

[42]  E. O'Brien,et al.  Handbook of Computational Group Theory , 2005 .

[43]  A. Björner,et al.  Combinatorics of Coxeter Groups , 2005 .

[44]  È. Vinberg,et al.  Discrete groups that are generated by reflections , 1971 .

[45]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[46]  David B. A. Epstein,et al.  The Linearity of the Conjugacy Problem in Word-hyperbolic Groups , 2006, Int. J. Algebra Comput..

[47]  Gabor Moussong,et al.  Hyperbolic Coxeter groups , 1988 .