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Original Articles

Howson property and one-relator groupsFootnote1

Pages 1057-1072 | Received 01 Apr 1997, Published online: 27 Jun 2007

References

  • Alonso , J. , Brady , T. , Cooper , D. , Ferlini , V. , Lustig , M. , Mihalik , M. , Shapiro , M. and Short , H. 1991 . “ Notes on hyperbolic groups, Group theory from a geometric viewpoint ” . In Proc. ICTP. Trieste 3 – 63 . World Scientific, , Singapore
  • Baumslag , B. 1966 . Intersections of Finitely Generated Subgroups in Free Products . J. London Math. Soc , 41 : 673 – 679 .
  • Brady , N. 1995 . Branched coverings of cubical complexes and subgroups of hyperbolic groups , University of Utah . preprint
  • Burns , R. 1972 . On finitely generated subgroups of an amalgamated product of two sub- groups . Trans. Amer. Math. Soc , 169 : 293 – 306 .
  • Burns , R. 1973 . Finitely generated subgroups of HNN groups . Canad. J. of Math , 25 : 1103 – 1112 .
  • Burns , R. and Brunner , A. 1979 . Two remarks on Howson’s group property . Algebra i Logika , 18 ( 5 ) : 513 – 522 .
  • Brunner , A. , Burns , R. and Solitar , D. 1984 . “ The subgroup separability of free products of two free groups with cyclic amalgamation ” . In Contributions to group theory Contemp. Math , Vol. 33 , 90 – 115 . Providence, R.I : Amer. Math. Soc .
  • Bestvina , M. and Feighn , M. 1992 . The Combination Theorem for Negatively Curved Groups . J. of DifF. Geom , 35 : 85 – 101 .
  • Bestvina , M. and Feighn , M. 1996 . Addendum and correction to:”A combination theo- rem for negatively curved groups” . J. DifF. Geom , 43 ( 4 ) : 783 – 788 .
  • Burns , R. , Karras , A. and Solitar , D. 1987 . A note on groups with separable finitely gen- erated subgroups . Bull. Austral. Math. Soc , 36 ( 1 ) : 153 – 160 .
  • Cohen , D. 1976 . Finitely generated subgroups of amalgamated products and HNN groups . J. Austr. Math. Soc, Ser A , 22 ( 1 ) : 274 – 281 .
  • Coornaert , M. , Delzant , T. and Papadopoulos , A. 1990 . “ Geometrie et theorie des groupes. Les groupes hyperboliques de Gromov ” . In Lecture Notes in Mathematics , Vol. 1441 , Berlin : Springer-Verlag .
  • Fischer , J. , Karrass , A. and Solitar , D. 1972 . On one-relator groups having elements of finite order . Proc Amer. Math. Soc , 33 : 297 – 301 .
  • Gitik , R. 1997 . On Quasiconvex Subgroups of Negatively Curved Groups . J. Pure and Appl. Algebra , 119 ( 2 ) : 155 – 169 .
  • Gitik , R. 1996 . On the combination theorem for negatively curved groups . Internat. J. Algebra Comput , 6 ( 6 ) : 751 – 760 .
  • Gromov , M. 1987 . “ Hyperbolic Groups ” . In Essays in group theory , Edited by: Gersten , S.M. Vol. 8 , 75 – 263 . Springer . MSRI Publ
  • Ghys , E. 1990 . Sur les groupes hyperboliques d’aprés Mikhael Gromov , Edited by: De La Harpe , P. Vol. 83 , Boston : Birkhäuser . Progress in Mathematics series
  • Gersten , S.M. and Short , H. 1990 . Small cancellation theory and automatic groups . Invent. Math , 102 ( 2 ) : 305 – 334 .
  • Hempel J. The finitely generated intersection property for Kleinian groups, Knot theory and manifolds Vancouver B.C. Springer Berlin, New York 1985 1144 18 24 Lecture Notes in Math 1983
  • Jaco , W. 1980 . “ Lectures on 3-manifold topology ” . In C.B.M.S. Series , Vol. 43 , Amer. Math. Soc .
  • Kapovich , I. 1996 . “ Quasiconvex subgroups of one-relator groups with torsion ” . In PhD Thesis , CUNY .
  • Kapovich , I. 1997 . Hyperbolic groups and amalgams . Intern. J. Alg. Comp , 7 ( 6 ) : 771 – 811 .
  • Kapovich , I. 1194/95 . A non-quasiconvex subgroup of a hyperbolic group with an exotic limit set . New York J. Math , 1 ( 6 ) : 184 – 195 .
  • Kharlampovich , O. and Myasnikov , A. 1998 . Hyperbolic groups and free constructions . Trans. Amer. Math. Soc , 350 ( 2 ) : 571 – 613 .
  • Kapovich , I. and Short , H. 1996 . Greenberg’s theorem for quasiconvex subgroups of word hyperbolic groups . Canad. J. Math , 48 ( 6 ) : 1224 – 1244 .
  • Karras , A. and Solitar , D. 1969 . On the failure of the Howson property for a group with a single defining relator . Math. Z , 108 ( 6 ) : 235 – 236 .
  • Karras , A. and Solitar , D. 1970 . The subgroups of a free product of two groups with an amalgamated subgroup . Trans. Am. Math. Soc , 150 ( 6 ) : 227 – 255 .
  • Karras , A. and Solitar , D. 1971 . Subgroups of HNN-groups and groups with one defining relation . Can. J. Math , 23 ( 6 ) : 627 – 643 .
  • Long , D. 1990 . Engulfing and subgroup separability for hyperbolic groups . Trans. Amer. Math. Soc , 320 ( 2 ) : 643 – 664 .
  • Long , D. and Niblo , G. 1991 . Subgroup separability and 3-rnanifold groups . Math. Z , 207 ( 2 ) : 209 – 215 .
  • Lyndon , R.C. and Schupp , P.E. 1977 . Combinatorial Group Theory , Berlin : Springer-Verlag . Heidleberg-New York
  • Group Theory Cooperative MAGNUS Computational package for exploring infinite groups, version 2.1.0(beta) City College of CUNY March 1997 (Baumslag, G., director)
  • Moldavanskii , D. 1968 . The intersection of finitely generated subgroups . Sibirsk. Mat. Z , 9 : 1422 – 1426 .
  • Mihalik , M. and Towle , W. 1995 . Quasiconvex subgroups of negatively curved groups . J. Pure and Appl. Algebra , 3 : 297 – 301 .
  • Pittet , Ch . 1993 . “ Surface groups and quasiconvexity ” . In Geometric Group Theory , Vol. 181 , 169 – 175 . Cambridge : Cambridge University Press . (Sussex 1991), London Math. Soc. Lecture Notes Series
  • Rips , E. 1982 . Subgroups of small cancellation groups . Bull.London Math.Soc , 14 : 45 – 47 .
  • Scott , P. 1978 . Subgroups of surface groups are almost geometric . J. London Math. Soc , 17 ( 3 ) : 555 – 565 .
  • Scott , P. 1985 . Subgroups of surface groups are almost geometric, correction . J. London Math. Soc , 32 ( 2 ) : 217 – 220 .
  • Short , H. 1991 . “ Quasiconvexity and a Theorem of Howson’s ” . In Group theory from a geo- metric viewpoint , World Scientific, , Singapore : Proc. ICTP. Trieste .
  • Swarup , G.A. 1993 . Geometric finiteness and rationality . J. of Pure and Appl. Algebra , 86 : 327 – 333 .
  • Thurston , W. 1982 . Three-dimensional manifolds, Kleinian groups and hyperbolic ge-ometry . Bull. Amer. Math. Soc. (N.S.) , 6 ( 3 ) : 357 – 381 .
  • Wong , P. 1993 . Subgroup separability of certain HNN extensions . Rocky Mountain J. Math , 23 ( 1 ) : 391 – 394 .

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