Lecture Notes in Mathematics

Transcription

1 Lecture Notes in Mathematics Edited by A. Oold and B. Eckmann 1281 O. H. Kegel F. Menegazzo G. Zacher (Eds.) Group Theory Proceedings of a Conference held at Brixen/Bressanone, Italy, May 25-31, 1986 Springer-Verlag Berlin Heidelberg New York London Paris Tokyo

2 Editors Otto H. Kegel Mathematisches Institut, Albert-Ludwiq-Universitat AlbertstraBe 23b, 7800 Freiburg, Federal Republic of Germany Federico Menegazzo Giovanni Zacher Seminario Matematico dell' Universita Via Belzoni, 7,35131 Padova, Italy Mathematics Subject Classification (1980): ISBN X Springer-Verlag Berlin Heidelberg New York ISBN X Springer-Verlag New York Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. Springer-Verlag Berlin Heidelberg 1987 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/

3 Pre f ace This volume presents the texts of most of the invited lectures and some of the contributions given at the International Conference on Group Theory which took place May 1986 at Brixen/ Bressanone, Italy, on the premises of the Casa della Gioventu Universitaria dell'universita di Padova. There were 15 invited lecturers. In the afternoon 24 shorter communications were given. In all, there were 78 participants. Beside the formal lectures there were intensive informal contacts, discussions and exchanges of ideas, often till late in the night The conference was supported financially by the Ministero della Pubblica Istruzione, by the C.N.R., by the University of Padova and by the C.I.R.M. (Trento); the latter also assumed responsibility for the local organisation and administration. We have to thank all the lecturers, participants, and the local organisers, whose enthusiasm and devotion made this meeting a success. o. H. Kegel, Freiburg F. Menegazzo, Padova G. Zacher, Padova

4 List of Participants 1. Bernhard AMBERG (Mainz) 2. Marco BARLOTTI (Firenze) 3. Claudio BARTOLONE (Palermo) 4. Mariagrazia BIANCHI (Milano) 5. Arrigo BONISOLI (Modena) 6. Rolf BRANDL (Wurzburg) 7. Brunella BRUNO (Padova) 8. Giorgio BUSETTO (Padova) 9. Andrea CARANTI (Trento) 10. Luisa CARINI (Messina) 11. Maria Rosaria CELENTANI (Napoli) 12. Gabriella CORSI TANI (Firenze) 13. Mario CURZIO (Napoli) 14. Alma D'ANIELLO (Mainz) 15. Rex DARK (Galway) 16. Francesco DE GIOVANNI (Napoli) 17. Lino DI MARTINO (Milano) 18. Walter DIRSCHERL (Wurzburg) 19. Maurizio EMALDI (Padova) 20. Valeria FEDRI (Firenze) 21. Giovanni FERRERO (Parma) 22. Silvana FRANCIOSI (Napoli) 23. Alberto FRIGERIO (Padova) 24. Antonino GIAMBRUNO (Palermo) 25. Anna GILLIO BERTA MAURI (Milano) 26. Anna Luisa GILOTTI (Firenze) 27. Fletcher GROSS (Salt Lake City) 28. Karl GRUENBERG (London) 29. Narain GUPTA (Winnipeg) 30. Brian HARTLEY (Manchester) 31. Trevor HAWKES (Warwick) 32. Hermann HEINEKEN (Wurzburg) 33. Wolfgang HERFORT (Wien) 34. Manfred J. KARBE (Berlin) 35. Otto KEGEL (Freiburg) 36. Enrico JABARA (Padova) 37. Hartmut LAUE (Kiel) 38. Felix LEINEN (Mainz) 39. John LENNOX (Cardiff) 40. Antonella LEONE (Napoli) 41. Patrizia LONGOBARDI (Napoli) 42. Andrea LUCCHINI (Padova) 43. Mercede MAJ (Napoli) 44. Ermanno MARCH lonna (Milano) 45. Sandro MATTAREI (Trento) 46. Federico MENEGAZZO (Padova) 47. Martin MENTH (Wurzburg) 48. Claudia METELLI (Padova) 49. Walter MOHRES (Wurzburg) 50. Carlo MORINI (Ferrara) 51. Franco NAPOLITANI (Padova)

5 52. Andreas NEUMANN (Trento) 53. Peter NEUMANN (Oxford) 54. Martin L. NEWELL (Galway) 55. Peter Pal PALFY (Budapest) 56. Virgilio PANNONE (Firenze) 57. Giuseppe PIRILLO (Firenze) 58. Peter PLAUMANN (Erlangen) 59. Salvatore RAO (Napoli) 60. Derek J.S. ROBINSON (Urbana) 61. Antonio ROSATI (Firenze) 62. James ROSEBLADE (Cambridge) 63. Roland SCHMIDT (Kiel) 64. Benedetto SCIMEMI (Padova) 65. Carlo M. SCOPPOLA (Trento) 66. Steward STONEHEWER (Warwick) 67. Luigi SERENA (Firenze) 68. M. Clara TAMBURINI BELLANI (Milano) 69. Umberto TIBERIO (Firenze) 70. Cesarina TIBILETTI MARCHIONNA (Milano) 71. Sean TOBIN (Galway) 72. Libero VERARDI (Bologna) 73. Erich WALTER (Trento) 74. John WILSON (Cambridge) 75. Giovanni ZACHER (Padova) 76. Vittoria ZAMBELLI (Milano) 77. Guido ZAPPA (Firenze) 78. Irene ZIMMERMANN (Freiburg) v

6 CONTENTS Preface List of Participants III IV BARLOTII, M. Faithful simple modules for the non-abelian group of orderpq CARANTI, A., FRANCIOSI, S. and F. de GIOVANNI. Some examples of infinite groups in which each element commutes with its endomorphic images GIAMBRUNO, A. Polynomial identities with involution and the hyperoctahedral group GROSS, F. Automorphisms of induced extensions GUPTA, C.K., GUPTA, N.D. and F. LEVIN. On dimension subgroups relative to certain product ideals HARTLEY, B. Centralizers in locally finite groups HAWKES, T. Subgroup embedding properties HEINEKEN, H. Soluble irreducible groups of automorphisms of certain groups of class two LAUE, H. On automorphism groups which normalize an abelian normal subgroup LEINEN, F. and R.E. PHILLIPS. Algebraically closed groups in locally finite group classes LENNOX, J.e. Soluble groups with nilpotent-extensible subgroups LONGOBARDI, P. and M. MAJ. On the nilpotence of groups with a certain lattice of normal subgroups MOHRES, W. Torsion-free nilpotent groups with bounded ranks of the abelian subgroups PIRILLO, G. On permutation properties for semigroups ROBINSON, D.J.S. Vanishing theorems for cohomology of locally nilpotent groups SCHMIDT, R. Untergruppenverbande endlicher auflosbarer Gruppen SCOPPOLA, e.m. An example of a nonabelian Frobenius-Wielandt complement STONEHEWER, S.E. Subnormal subgroups of factorised groups WILSON, J.S. An embedding condition for subgroups of infinite groups